There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{3} + e + 4x - ln(2{x}^{(\frac{({3}^{\frac{1}{2}})}{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3} + e + 4x - ln(2{x}^{(3^{\frac{1}{2}}*\frac{1}{2})})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3} + e + 4x - ln(2{x}^{(3^{\frac{1}{2}}*\frac{1}{2})})\right)}{dx}\\=&3x^{2} + 0 + 4 - \frac{2({x}^{(3^{\frac{1}{2}}*\frac{1}{2})}((0)ln(x) + \frac{(3^{\frac{1}{2}}*\frac{1}{2})(1)}{(x)}))}{(2{x}^{(3^{\frac{1}{2}}*\frac{1}{2})})}\\=&3x^{2} - \frac{3^{\frac{1}{2}}{x}^{(\frac{5}{2}^{\frac{1}{2}}*\frac{1}{2})}}{2x} + 4\\ \end{split}\end{equation} \]

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