There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {tan(x)}^{2} - {cos(x)}^{3} + sqrt(lg_{tan(x)}^{arcsin(5)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = tan^{2}(x) - cos^{3}(x) + sqrt(lg_{tan(x)}^{arcsin(5)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan^{2}(x) - cos^{3}(x) + sqrt(lg_{tan(x)}^{arcsin(5)})\right)}{dx}\\=&2tan(x)sec^{2}(x)(1) - -3cos^{2}(x)sin(x) + \frac{sec^{2}(x)(1)*\frac{1}{2}}{ln{10}(tan(x))(lg_{tan(x)}^{arcsin(5)})^{\frac{1}{2}}}\\=&2tan(x)sec^{2}(x) + 3sin(x)cos^{2}(x) + \frac{sec^{2}(x)}{2ln{10}lg^{\frac{1}{2}}(tan(x), arcsin(5))tan(x)}\\ \end{split}\end{equation} \]

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