There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ tan(sin(sqrt(\frac{x}{(1 + x)})))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = tan(sin(sqrt(\frac{x}{(x + 1)})))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan(sin(sqrt(\frac{x}{(x + 1)})))\right)}{dx}\\=&sec^{2}(sin(sqrt(\frac{x}{(x + 1)})))(\frac{cos(sqrt(\frac{x}{(x + 1)}))((\frac{-(1 + 0)}{(x + 1)^{2}})x + \frac{1}{(x + 1)})*\frac{1}{2}}{(\frac{x}{(x + 1)})^{\frac{1}{2}}})\\=&\frac{-x^{\frac{1}{2}}cos(sqrt(\frac{x}{(x + 1)}))sec^{2}(sin(sqrt(\frac{x}{(x + 1)})))}{2(x + 1)^{\frac{3}{2}}} + \frac{cos(sqrt(\frac{x}{(x + 1)}))sec^{2}(sin(sqrt(\frac{x}{(x + 1)})))}{2(x + 1)^{\frac{1}{2}}x^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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