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

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