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

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