There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{sin(arctan({x}^{100}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{sin(arctan(x^{100}))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{sin(arctan(x^{100}))}\right)}{dx}\\=&e^{sin(arctan(x^{100}))}cos(arctan(x^{100}))(\frac{(100x^{99})}{(1 + (x^{100})^{2})})\\=&\frac{100x^{99}e^{sin(arctan(x^{100}))}cos(arctan(x^{100}))}{(x^{200} + 1)}\\ \end{split}\end{equation} \]

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