There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ x + sqrt({x}^{2} + 10sqrt(3)x + 100)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x + sqrt(10xsqrt(3) + x^{2} + 100)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x + sqrt(10xsqrt(3) + x^{2} + 100)\right)}{dx}\\=&1 + \frac{(10sqrt(3) + 10x*0*\frac{1}{2}*3^{\frac{1}{2}} + 2x + 0)*\frac{1}{2}}{(10xsqrt(3) + x^{2} + 100)^{\frac{1}{2}}}\\=&\frac{5sqrt(3)}{(10xsqrt(3) + x^{2} + 100)^{\frac{1}{2}}} + \frac{x}{(10xsqrt(3) + x^{2} + 100)^{\frac{1}{2}}} + 1\\ \end{split}\end{equation} \]

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