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 3 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {e}^{(sin(\frac{{x}^{2}}{360}) + cos(3x + \frac{{x}^{2}}{150}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}\right)}{dx}\\=&({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))\\=&\frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})}{180} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{75} - 3{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})}{180} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{75} - 3{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})\right)}{dx}\\=&\frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})}{180} + \frac{x({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))cos(\frac{1}{360}x^{2})}{180} + \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*-sin(\frac{1}{360}x^{2})*\frac{1}{360}*2x}{180} - \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{75} - \frac{x({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin(3x + \frac{1}{150}x^{2})}{75} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)}{75} - 3({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin(3x + \frac{1}{150}x^{2}) - 3{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)\\=&\frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})}{180} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos^{2}(\frac{1}{360}x^{2})}{32400} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{6750} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{30} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(\frac{1}{360}x^{2})}{32400} - \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{75} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{5625} + \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{25} - \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{25} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{5625} + 9{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2}) - 9{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})}{180} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos^{2}(\frac{1}{360}x^{2})}{32400} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{6750} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{30} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(\frac{1}{360}x^{2})}{32400} - \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{75} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{5625} + \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{25} - \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{25} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{5625} + 9{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2}) - 9{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})\right)}{dx}\\=&\frac{({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))cos(\frac{1}{360}x^{2})}{180} + \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*-sin(\frac{1}{360}x^{2})*\frac{1}{360}*2x}{180} + \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos^{2}(\frac{1}{360}x^{2})}{32400} + \frac{x^{2}({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))cos^{2}(\frac{1}{360}x^{2})}{32400} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*-2cos(\frac{1}{360}x^{2})sin(\frac{1}{360}x^{2})*\frac{1}{360}*2x}{32400} - \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{6750} - \frac{x^{2}({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{6750} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)cos(\frac{1}{360}x^{2})}{6750} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})*-sin(\frac{1}{360}x^{2})*\frac{1}{360}*2x}{6750} - \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{30} - \frac{x({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{30} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)cos(\frac{1}{360}x^{2})}{30} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})*-sin(\frac{1}{360}x^{2})*\frac{1}{360}*2x}{30} - \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(\frac{1}{360}x^{2})}{32400} - \frac{x^{2}({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin(\frac{1}{360}x^{2})}{32400} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x}{32400} - \frac{({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin(3x + \frac{1}{150}x^{2})}{75} - \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)}{75} + \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{5625} + \frac{x^{2}({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin^{2}(3x + \frac{1}{150}x^{2})}{5625} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*2sin(3x + \frac{1}{150}x^{2})cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)}{5625} + \frac{2{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{25} + \frac{2x({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin^{2}(3x + \frac{1}{150}x^{2})}{25} + \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*2sin(3x + \frac{1}{150}x^{2})cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)}{25} - \frac{2{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{25} - \frac{2x({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))cos(3x + \frac{1}{150}x^{2})}{25} - \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*-sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)}{25} - \frac{2x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{5625} - \frac{x^{2}({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))cos(3x + \frac{1}{150}x^{2})}{5625} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*-sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)}{5625} + 9({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))sin^{2}(3x + \frac{1}{150}x^{2}) + 9{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*2sin(3x + \frac{1}{150}x^{2})cos(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x) - 9({e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}((cos(\frac{1}{360}x^{2})*\frac{1}{360}*2x + -sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x))ln(e) + \frac{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))(0)}{(e)}))cos(3x + \frac{1}{150}x^{2}) - 9{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}*-sin(3x + \frac{1}{150}x^{2})(3 + \frac{1}{150}*2x)\\=& - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{1125} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{2250} - \frac{{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{20} - \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(\frac{1}{360}x^{2})cos(\frac{1}{360}x^{2})}{1944000} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{10} - \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{506250} - \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos^{2}(\frac{1}{360}x^{2})}{810000} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos^{2}(\frac{1}{360}x^{2})}{3600} + \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(\frac{1}{360}x^{2})sin(3x + \frac{1}{150}x^{2})}{1215000} + \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{337500} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{750} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})cos(3x + \frac{1}{150}x^{2})}{2250} - \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})cos(3x + \frac{1}{150}x^{2})}{1012500} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(\frac{1}{360}x^{2})sin(3x + \frac{1}{150}x^{2})}{5400} + \frac{3x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})cos(\frac{1}{360}x^{2})}{20} + \frac{3x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(3x + \frac{1}{150}x^{2})}{625} + \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})sin(\frac{1}{360}x^{2})}{2430000} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})sin(\frac{1}{360}x^{2})}{10800} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})cos(3x + \frac{1}{150}x^{2})}{20} + \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(3x + \frac{1}{150}x^{2})}{140625} + 81{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(3x + \frac{1}{150}x^{2}) - \frac{3{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{25} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(3x + \frac{1}{150}x^{2})}{1875} + \frac{27x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})cos(3x + \frac{1}{150}x^{2})}{25} - \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{3}(3x + \frac{1}{150}x^{2})}{421875} - \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{3}(3x + \frac{1}{150}x^{2})}{625} + \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{1875} + \frac{3{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{2}(3x + \frac{1}{150}x^{2})}{25} - \frac{9x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{3}(3x + \frac{1}{150}x^{2})}{25} - \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(\frac{1}{360}x^{2})}{10800} + \frac{x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos^{2}(\frac{1}{360}x^{2})}{10800} + \frac{x^{2}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{625} + \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos^{3}(\frac{1}{360}x^{2})}{5832000} + \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{421875} - 27{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin^{3}(3x + \frac{1}{150}x^{2}) + \frac{9x{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})}{25} - \frac{x^{3}{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}cos(\frac{1}{360}x^{2})}{5832000} + 27{e}^{(sin(\frac{1}{360}x^{2}) + cos(3x + \frac{1}{150}x^{2}))}sin(3x + \frac{1}{150}x^{2})\\ \end{split}\end{equation} \]