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

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