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 1 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (2xcos({x}^{2} + {y}^{2}) - \frac{1}{10}(2x + y + 2)sin({x}^{2} + {y}^{2})){e}^{(\frac{-1}{10}({x}^{2} + {y}^{2} + xy + 2x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) - \frac{1}{5}x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{10}y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) - \frac{1}{5}x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{10}y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})\right)}{dx}\\=&2{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) + 2x({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))cos(x^{2} + y^{2}) + 2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}*-sin(x^{2} + y^{2})(2x + 0) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{5}x({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))sin(x^{2} + y^{2}) - \frac{1}{5}x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})(2x + 0) - \frac{1}{10}y({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))sin(x^{2} + y^{2}) - \frac{1}{10}y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})(2x + 0) - \frac{1}{5}({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))sin(x^{2} + y^{2}) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})(2x + 0)\\=&2{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) - \frac{4x^{2}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})}{5} - \frac{2yx{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})}{5} - \frac{4x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})}{5} - \frac{99x^{2}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} - \frac{4{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} + \frac{yx{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} + \frac{2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} + \frac{y^{2}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{100} + \frac{y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (2xcos({x}^{2} + {y}^{2}) - \frac{1}{10}(2x + y + 2)sin({x}^{2} + {y}^{2})){e}^{(\frac{-1}{10}({x}^{2} + {y}^{2} + xy + 2x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) - \frac{1}{5}x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{10}y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) - \frac{1}{5}x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{10}y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})\right)}{dx}\\=&2{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) + 2x({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))cos(x^{2} + y^{2}) + 2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}*-sin(x^{2} + y^{2})(2x + 0) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2}) - \frac{1}{5}x({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))sin(x^{2} + y^{2}) - \frac{1}{5}x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})(2x + 0) - \frac{1}{10}y({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))sin(x^{2} + y^{2}) - \frac{1}{10}y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})(2x + 0) - \frac{1}{5}({e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}((\frac{-1}{10}*2x - \frac{1}{10}y + 0 - \frac{1}{5})ln(e) + \frac{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)(0)}{(e)}))sin(x^{2} + y^{2}) - \frac{1}{5}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})(2x + 0)\\=&2{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2}) - \frac{4x^{2}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})}{5} - \frac{2yx{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})}{5} - \frac{4x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}cos(x^{2} + y^{2})}{5} - \frac{99x^{2}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} - \frac{4{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} + \frac{yx{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} + \frac{2x{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25} + \frac{y^{2}{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{100} + \frac{y{e}^{(\frac{-1}{10}x^{2} - \frac{1}{10}yx - \frac{1}{10}y^{2} - \frac{1}{5}x)}sin(x^{2} + y^{2})}{25}\\ \end{split}\end{equation} \]