Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {({x}^{2} - x - 1)}^{(x + 2)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{2} - x - 1)^{(x + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))\\=&(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{2x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{3x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{2x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{3x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1) + \frac{(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)} + 2(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x^{2}(x^{2} - x - 1)^{(x + 2)} + \frac{2*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{2x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} + 3(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)} + \frac{3(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{3x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} - 2(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)} - \frac{2((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)}\\=&(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{4x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{4(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{8x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{4x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{5x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{4x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{4(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{8x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{4x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{5x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1) + \frac{(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)} + 4(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{4*2x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{4x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{4x^{2}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} - 4(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) - \frac{4((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{4(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)} + \frac{6(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{6x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} + 2(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)} + \frac{2((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} + 8(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{3}(x^{2} - x - 1)^{(x + 2)} + \frac{8*3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{8x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} - 3(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{2}(x^{2} - x - 1)^{(x + 2)} - \frac{3*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{3x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 4(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{4}(x^{2} - x - 1)^{(x + 2)} + \frac{4*4x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{4x^{4}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} - 5(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x(x^{2} - x - 1)^{(x + 2)} - \frac{5(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{5x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 2(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})(x^{2} - x - 1)^{(x + 2)} + \frac{2((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}}\\=&(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1) + \frac{6x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{6(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{24x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{36x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{42x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{24x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{3(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{14x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{7x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{12x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{8x^{6}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1) + \frac{6x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{6(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{24x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{36x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{42x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{24x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{3(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{14x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{7x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{12x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{8x^{6}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{3}(x^{2} - x - 1) + \frac{(x^{2} - x - 1)^{(x + 2)}*3ln^{2}(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{6*2x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x^{2}(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 9(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{9(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} - 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) - \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{6(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 18(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{18(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 24(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{24*3x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24x^{3}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} - 9(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) - \frac{9*2x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} + 12(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{12*4x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} - 15(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) - \frac{15(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} + 36(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{3}(x^{2} - x - 1)^{(x + 2)} + \frac{36*3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{36x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 42(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{2}(x^{2} - x - 1)^{(x + 2)} + \frac{42*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{42x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} - 24(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x(x^{2} - x - 1)^{(x + 2)} - \frac{24(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{24x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 6(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} - 3(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})(x^{2} - x - 1)^{(x + 2)} - \frac{3((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)} + \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} - 14(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{4}(x^{2} - x - 1)^{(x + 2)} - \frac{14*4x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{14x^{4}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} - 7(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{3}(x^{2} - x - 1)^{(x + 2)} - \frac{7*3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{7x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} + 12(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{5}(x^{2} - x - 1)^{(x + 2)} + \frac{12*5x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{12x^{5}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} + 9(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{2}(x^{2} - x - 1)^{(x + 2)} + \frac{9*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{9x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} + 8(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{6}(x^{2} - x - 1)^{(x + 2)} + \frac{8*6x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{8x^{6}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} - 2(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x(x^{2} - x - 1)^{(x + 2)} - \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{2x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}}\\=&(x^{2} - x - 1)^{(x + 2)}ln^{4}(x^{2} - x - 1) + \frac{8x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{12x(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{8(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{36x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{12(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{48x^{3}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24x^{4}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{18x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{144x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{168x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{30x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{96x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{12(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{56x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} - \frac{28x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} - \frac{8x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{36x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{48x^{5}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{32x^{6}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{156x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{144x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{188x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{24x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{84x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{144x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{48x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{36(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{8(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{40x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} + \frac{25x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} - \frac{56x^{6}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} - \frac{38x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} + \frac{15x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} + \frac{16x^{8}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} - \frac{2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {({x}^{2} - x - 1)}^{(x + 2)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{2} - x - 1)^{(x + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))\\=&(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{2x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{3x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{2x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{3x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1) + \frac{(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)} + 2(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x^{2}(x^{2} - x - 1)^{(x + 2)} + \frac{2*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{2x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} + 3(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)} + \frac{3(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{3x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} - 2(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)} - \frac{2((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)}\\=&(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{4x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{4(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{8x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{4x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{5x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{4x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{4(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{8x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{4x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{5x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1) + \frac{(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)} + 4(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{4*2x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{4x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{4x^{2}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} - 4(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) - \frac{4((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{4(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)} + \frac{6(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} + \frac{6x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} + 2(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)} + \frac{2((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} + 8(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{3}(x^{2} - x - 1)^{(x + 2)} + \frac{8*3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{8x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} - 3(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{2}(x^{2} - x - 1)^{(x + 2)} - \frac{3*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{3x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 4(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{4}(x^{2} - x - 1)^{(x + 2)} + \frac{4*4x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{4x^{4}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} - 5(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x(x^{2} - x - 1)^{(x + 2)} - \frac{5(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{5x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 2(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})(x^{2} - x - 1)^{(x + 2)} + \frac{2((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}}\\=&(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1) + \frac{6x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{6(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{24x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{36x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{42x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{24x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{3(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{14x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{7x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{12x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{8x^{6}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( (x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1) + \frac{6x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{6(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{24x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{36x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{42x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{24x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{3(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)} - \frac{14x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{7x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{12x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{8x^{6}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}}\right)}{dx}\\=&((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{3}(x^{2} - x - 1) + \frac{(x^{2} - x - 1)^{(x + 2)}*3ln^{2}(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{6*2x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6x^{2}(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 9(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) + \frac{9(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{9x(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} - 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1) - \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{6(x^{2} - x - 1)^{(x + 2)}*2ln(x^{2} - x - 1)(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 18(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{18(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{18x(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{6(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)(x^{2} - x - 1)} + 24(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{24*3x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24x^{3}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} - 9(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) - \frac{9*2x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{9x^{2}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} + 12(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{12*4x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12x^{4}(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} - 15(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) - \frac{15(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{15x(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} + 36(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{3}(x^{2} - x - 1)^{(x + 2)} + \frac{36*3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{36x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 42(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x^{2}(x^{2} - x - 1)^{(x + 2)} + \frac{42*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{42x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} - 24(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})x(x^{2} - x - 1)^{(x + 2)} - \frac{24(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{24x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 6(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1) + \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{6(x^{2} - x - 1)^{(x + 2)}(2x - 1 + 0)}{(x^{2} - x - 1)^{2}(x^{2} - x - 1)} - 3(\frac{-2(2x - 1 + 0)}{(x^{2} - x - 1)^{3}})(x^{2} - x - 1)^{(x + 2)} - \frac{3((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{2}} + 6(\frac{-(2x - 1 + 0)}{(x^{2} - x - 1)^{2}})(x^{2} - x - 1)^{(x + 2)} + \frac{6((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)} - 14(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{4}(x^{2} - x - 1)^{(x + 2)} - \frac{14*4x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{14x^{4}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} - 7(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{3}(x^{2} - x - 1)^{(x + 2)} - \frac{7*3x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{7x^{3}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} + 12(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{5}(x^{2} - x - 1)^{(x + 2)} + \frac{12*5x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{12x^{5}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} + 9(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{2}(x^{2} - x - 1)^{(x + 2)} + \frac{9*2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{9x^{2}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} + 8(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x^{6}(x^{2} - x - 1)^{(x + 2)} + \frac{8*6x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{8x^{6}((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}} - 2(\frac{-3(2x - 1 + 0)}{(x^{2} - x - 1)^{4}})x(x^{2} - x - 1)^{(x + 2)} - \frac{2(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{2x((x^{2} - x - 1)^{(x + 2)}((1 + 0)ln(x^{2} - x - 1) + \frac{(x + 2)(2x - 1 + 0)}{(x^{2} - x - 1)}))}{(x^{2} - x - 1)^{3}}\\=&(x^{2} - x - 1)^{(x + 2)}ln^{4}(x^{2} - x - 1) + \frac{8x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{12x(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{8(x^{2} - x - 1)^{(x + 2)}ln^{3}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{36x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{12(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)} + \frac{48x^{3}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24x^{4}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{18x^{2}(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{144x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{168x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{30x(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{96x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{12(x^{2} - x - 1)^{(x + 2)}ln^{2}(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} - \frac{12(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{2}} + \frac{24(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)} - \frac{56x^{4}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} - \frac{28x^{3}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} - \frac{8x(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{36x^{2}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{48x^{5}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{32x^{6}(x^{2} - x - 1)^{(x + 2)}ln(x^{2} - x - 1)}{(x^{2} - x - 1)^{3}} + \frac{156x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{144x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{188x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{24x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{84x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} + \frac{144x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{48x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} - \frac{36(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{2}} - \frac{8(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{3}} + \frac{40x^{5}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} + \frac{25x^{4}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} - \frac{56x^{6}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} - \frac{38x^{3}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} + \frac{15x^{2}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} + \frac{16x^{8}(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}} - \frac{2x(x^{2} - x - 1)^{(x + 2)}}{(x^{2} - x - 1)^{4}}\\ \end{split}\end{equation} \]