There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (sin(5x))({(tan({x}^{2}) - x)}^{3})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(5x)tan^{3}(x^{2}) - 3xsin(5x)tan^{2}(x^{2}) + 3x^{2}sin(5x)tan(x^{2}) - x^{3}sin(5x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(5x)tan^{3}(x^{2}) - 3xsin(5x)tan^{2}(x^{2}) + 3x^{2}sin(5x)tan(x^{2}) - x^{3}sin(5x)\right)}{dx}\\=&cos(5x)*5tan^{3}(x^{2}) + sin(5x)*3tan^{2}(x^{2})sec^{2}(x^{2})(2x) - 3sin(5x)tan^{2}(x^{2}) - 3xcos(5x)*5tan^{2}(x^{2}) - 3xsin(5x)*2tan(x^{2})sec^{2}(x^{2})(2x) + 3*2xsin(5x)tan(x^{2}) + 3x^{2}cos(5x)*5tan(x^{2}) + 3x^{2}sin(5x)sec^{2}(x^{2})(2x) - 3x^{2}sin(5x) - x^{3}cos(5x)*5\\=&5cos(5x)tan^{3}(x^{2}) + 6xsin(5x)tan^{2}(x^{2})sec^{2}(x^{2}) - 3sin(5x)tan^{2}(x^{2}) - 15xcos(5x)tan^{2}(x^{2}) - 12x^{2}sin(5x)tan(x^{2})sec^{2}(x^{2}) + 6xsin(5x)tan(x^{2}) + 15x^{2}cos(5x)tan(x^{2}) + 6x^{3}sin(5x)sec^{2}(x^{2}) - 3x^{2}sin(5x) - 5x^{3}cos(5x)\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！