Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 1 derivative of z is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (4({z}^{3}) - ({z}^{2}))({e}^{\frac{1}{z}})\ with\ respect\ to\ z:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4z^{3}{e}^{\frac{1}{z}} - z^{2}{e}^{\frac{1}{z}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 4z^{3}{e}^{\frac{1}{z}} - z^{2}{e}^{\frac{1}{z}}\right)}{dz}\\=&4*3z^{2}{e}^{\frac{1}{z}} + 4z^{3}({e}^{\frac{1}{z}}((\frac{-1}{z^{2}})ln(e) + \frac{(\frac{1}{z})(0)}{(e)})) - 2z{e}^{\frac{1}{z}} - z^{2}({e}^{\frac{1}{z}}((\frac{-1}{z^{2}})ln(e) + \frac{(\frac{1}{z})(0)}{(e)}))\\=&12z^{2}{e}^{\frac{1}{z}} - 6z{e}^{\frac{1}{z}} + {e}^{\frac{1}{z}}\\ \end{split}\end{equation} \]





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