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

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