There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 2xtan(x){sec(({x}^{2})tan(x))}^{2} + {x}^{2}{(sec(x))}^{2}{(sec(({x}^{2})tan(x)))}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2xtan(x)sec^{2}(x^{2}tan(x)) + x^{2}sec^{2}(x)sec^{2}(x^{2}tan(x))\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 2xtan(x)sec^{2}(x^{2}tan(x)) + x^{2}sec^{2}(x)sec^{2}(x^{2}tan(x))\right)}{dx}\\=&2tan(x)sec^{2}(x^{2}tan(x)) + 2xsec^{2}(x)(1)sec^{2}(x^{2}tan(x)) + 2xtan(x)*2sec^{2}(x^{2}tan(x))tan(x^{2}tan(x))(2xtan(x) + x^{2}sec^{2}(x)(1)) + 2xsec^{2}(x)sec^{2}(x^{2}tan(x)) + x^{2}*2sec^{2}(x)tan(x)sec^{2}(x^{2}tan(x)) + x^{2}sec^{2}(x)*2sec^{2}(x^{2}tan(x))tan(x^{2}tan(x))(2xtan(x) + x^{2}sec^{2}(x)(1))\\=&2tan(x)sec^{2}(x^{2}tan(x)) + 4xsec^{2}(x)sec^{2}(x^{2}tan(x)) + 4x^{3}tan(x^{2}tan(x))tan(x)sec^{2}(x)sec^{2}(x^{2}tan(x)) + 4x^{3}tan(x^{2}tan(x))tan(x)sec^{2}(x^{2}tan(x))sec^{2}(x) + 2x^{2}tan(x)sec^{2}(x)sec^{2}(x^{2}tan(x)) + 8x^{2}tan(x^{2}tan(x))tan^{2}(x)sec^{2}(x^{2}tan(x)) + 2x^{4}tan(x^{2}tan(x))sec^{4}(x)sec^{2}(x^{2}tan(x))\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!