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

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