There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(1 + sin(x)sin(x)) - 6{(2 - cos(x))}^{\frac{1}{3}} + 6\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(sin^{2}(x) + 1) - 6(-cos(x) + 2)^{\frac{1}{3}} + 6\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(sin^{2}(x) + 1) - 6(-cos(x) + 2)^{\frac{1}{3}} + 6\right)}{dx}\\=&\frac{(2sin(x)cos(x) + 0)}{(sin^{2}(x) + 1)} - 6(\frac{\frac{1}{3}(--sin(x) + 0)}{(-cos(x) + 2)^{\frac{2}{3}}}) + 0\\=&\frac{2sin(x)cos(x)}{(sin^{2}(x) + 1)} - \frac{2sin(x)}{(-cos(x) + 2)^{\frac{2}{3}}}\\ \end{split}\end{equation} \]

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