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

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