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

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