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

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