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

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