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

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