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

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