There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(1 + x)}^{5} - \frac{1}{sin(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{5} + 5x^{4} + 10x^{3} + 10x^{2} + 5x - \frac{1}{sin(x)} + 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{5} + 5x^{4} + 10x^{3} + 10x^{2} + 5x - \frac{1}{sin(x)} + 1\right)}{dx}\\=&5x^{4} + 5*4x^{3} + 10*3x^{2} + 10*2x + 5 - \frac{-cos(x)}{sin^{2}(x)} + 0\\=&5x^{4} + 20x^{3} + 30x^{2} + 20x + \frac{cos(x)}{sin^{2}(x)} + 5\\ \end{split}\end{equation} \]

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