There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (10ln(x + 1) + 30){x}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 10x^{\frac{1}{2}}ln(x + 1) + 30x^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 10x^{\frac{1}{2}}ln(x + 1) + 30x^{\frac{1}{2}}\right)}{dx}\\=&\frac{10*\frac{1}{2}ln(x + 1)}{x^{\frac{1}{2}}} + \frac{10x^{\frac{1}{2}}(1 + 0)}{(x + 1)} + \frac{30*\frac{1}{2}}{x^{\frac{1}{2}}}\\=&\frac{5ln(x + 1)}{x^{\frac{1}{2}}} + \frac{10x^{\frac{1}{2}}}{(x + 1)} + \frac{15}{x^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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