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

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