There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{1}{2})tan(\frac{arcsin(sqrt(x + 3))}{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}tan(\frac{1}{2}arcsin(sqrt(x + 3)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}tan(\frac{1}{2}arcsin(sqrt(x + 3)))\right)}{dx}\\=&\frac{1}{2}sec^{2}(\frac{1}{2}arcsin(sqrt(x + 3)))(\frac{1}{2}(\frac{(\frac{(1 + 0)*\frac{1}{2}}{(x + 3)^{\frac{1}{2}}})}{((1 - (sqrt(x + 3))^{2})^{\frac{1}{2}})}))\\=&\frac{sec^{2}(\frac{1}{2}arcsin(sqrt(x + 3)))}{8(-sqrt(x + 3)^{2} + 1)^{\frac{1}{2}}(x + 3)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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