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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ xtan(sin(cos(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xtan(sin(cos(x)))\right)}{dx}\\=&tan(sin(cos(x))) + xsec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))\\=&tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\right)}{dx}\\=&sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x)) - sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-2cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 2sin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 2sin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - x*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) - xcos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - xsin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-3*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3cos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3cos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3cos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 6*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin(x)cos(cos(x))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xcos(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)cos(cos(x))*-sin(x)cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xcos(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + x*3sin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin^{3}(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*3sin^{2}(x)cos(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)cos(cos(x))*-sin(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)*-sin(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))*3sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 2sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2x*3sin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)sec^{4}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))*4sec^{4}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 4sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4x*3sin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))*2tan(sin(cos(x)))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&4sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 12sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 8sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 8sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 16sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 16xsin^{4}(x)cos^{4}(cos(x))tan(sin(cos(x)))sec^{4}(sin(cos(x))) - 3xsin(cos(x))cos^{2}(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(cos(x))cos(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)sin(cos(x))sec^{2}(sin(cos(x))) + 6xsin(cos(x))sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6xcos^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 12xsin(cos(x))sin^{2}(x)cos(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{2}(x)cos^{3}(cos(x))cos(x)sec^{4}(sin(cos(x))) - 16xsin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{4}(x)sec^{2}(sin(cos(x))) - 8xsin^{4}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 18xsin^{2}(x)sin(cos(x))cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(cos(x))sin^{4}(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 16xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{2}(x)cos^{3}(cos(x))cos(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin^{4}(x)sin^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 8xsin^{4}(x)cos^{4}(cos(x))tan^{3}(sin(cos(x)))sec^{2}(sin(cos(x)))\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ xtan(sin(cos(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xtan(sin(cos(x)))\right)}{dx}\\=&tan(sin(cos(x))) + xsec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))\\=&tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( tan(sin(cos(x))) - xsin(x)cos(cos(x))sec^{2}(sin(cos(x)))\right)}{dx}\\=&sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x)) - sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -2sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-2cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 2sin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 2sin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - x*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - xcos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - xcos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) - xcos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - xsin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - xsin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&-3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -3cos(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x)))\right)}{dx}\\=&-3*-sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 3cos(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3cos(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3cos(cos(x))*-sin(x)sin^{2}(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))*2sin(x)cos(x)sec^{2}(sin(cos(x))) - 3sin(cos(x))sin^{2}(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 6*2sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 6sin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin(x)cos(cos(x))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 3sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xcos(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)cos(cos(x))*-sin(x)cos(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) - 3xsin(x)sin(cos(x))cos(x)*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xcos(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)*-2cos(cos(x))sin(cos(x))*-sin(x)cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + x*3sin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin^{3}(x)*-sin(cos(x))*-sin(x)sec^{2}(sin(cos(x))) + xsin^{3}(x)cos(cos(x))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 2sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2x*3sin^{2}(x)cos(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)cos(cos(x))*-sin(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 2xsin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)*-sin(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)*-2cos(cos(x))sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) + 4sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xcos(cos(x))*-sin(x)sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))*3sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)*-sin(cos(x))*-sin(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) + 4xsin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 2sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2x*3sin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 2xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)sec^{4}(sin(cos(x))) - 2xsin^{3}(x)cos^{3}(cos(x))*4sec^{4}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x) - 4sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4x*3sin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)*-3cos^{2}(cos(x))sin(cos(x))*-sin(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))*2tan(sin(cos(x)))sec^{2}(sin(cos(x)))(cos(cos(x))*-sin(x))sec^{2}(sin(cos(x))) - 4xsin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))*2sec^{2}(sin(cos(x)))tan(sin(cos(x)))cos(cos(x))*-sin(x)\\=&4sin(x)cos(cos(x))sec^{2}(sin(cos(x))) - 12sin(x)sin(cos(x))cos(x)sec^{2}(sin(cos(x))) + 8sin(x)cos^{2}(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 4sin^{3}(x)cos(cos(x))sec^{2}(sin(cos(x))) + 8sin^{3}(x)sin(cos(x))cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(x)cos(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 16sin(cos(x))sin^{3}(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8sin^{3}(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 16sin^{3}(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + xcos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{2}(x)sec^{2}(sin(cos(x))) + 16xsin^{4}(x)cos^{4}(cos(x))tan(sin(cos(x)))sec^{4}(sin(cos(x))) - 3xsin(cos(x))cos^{2}(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(cos(x))cos(x)sec^{2}(sin(cos(x))) + 3xsin^{2}(x)sin(cos(x))sec^{2}(sin(cos(x))) + 6xsin(cos(x))sin^{2}(x)cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 6xcos^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 12xsin(cos(x))sin^{2}(x)cos(cos(x))cos(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 8xsin^{2}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{2}(x)cos^{3}(cos(x))cos(x)sec^{4}(sin(cos(x))) - 16xsin^{2}(x)cos(x)cos^{3}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 3xsin^{2}(x)cos(x)cos(cos(x))sec^{2}(sin(cos(x))) + xsin(cos(x))sin^{4}(x)sec^{2}(sin(cos(x))) - 8xsin^{4}(x)cos^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 18xsin^{2}(x)sin(cos(x))cos(x)cos(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) + 2xsin^{2}(cos(x))sin^{4}(x)tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 2xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 16xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin^{2}(x)cos(x)cos^{3}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{2}(x)cos^{3}(cos(x))cos(x)tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 4xsin^{4}(x)sin^{2}(cos(x))tan(sin(cos(x)))sec^{2}(sin(cos(x))) - 10xsin(cos(x))sin^{4}(x)cos^{2}(cos(x))sec^{4}(sin(cos(x))) - 8xsin^{4}(x)sin(cos(x))cos^{2}(cos(x))tan^{2}(sin(cos(x)))sec^{2}(sin(cos(x))) + 8xsin^{4}(x)cos^{4}(cos(x))tan^{3}(sin(cos(x)))sec^{2}(sin(cos(x)))\\ \end{split}\end{equation} \]