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 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {2}^{({e}^{2}{\frac{1}{x}}^{2})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {2}^{(\frac{e^{2}}{x^{2}})}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( {2}^{(\frac{e^{2}}{x^{2}})}\right)}{dx}\\=&({2}^{(\frac{e^{2}}{x^{2}})}((\frac{-2e^{2}}{x^{3}} + \frac{2e*0}{x^{2}})ln(2) + \frac{(\frac{e^{2}}{x^{2}})(0)}{(2)}))\\=&\frac{-2 * {2}^{(\frac{e^{2}}{x^{2}})}e^{2}ln(2)}{x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2 * {2}^{(\frac{e^{2}}{x^{2}})}e^{2}ln(2)}{x^{3}}\right)}{dx}\\=&\frac{-2*-3 * {2}^{(\frac{e^{2}}{x^{2}})}e^{2}ln(2)}{x^{4}} - \frac{2({2}^{(\frac{e^{2}}{x^{2}})}((\frac{-2e^{2}}{x^{3}} + \frac{2e*0}{x^{2}})ln(2) + \frac{(\frac{e^{2}}{x^{2}})(0)}{(2)}))e^{2}ln(2)}{x^{3}} - \frac{2 * {2}^{(\frac{e^{2}}{x^{2}})}*2e*0ln(2)}{x^{3}} - \frac{2 * {2}^{(\frac{e^{2}}{x^{2}})}e^{2}*0}{x^{3}(2)}\\=&\frac{6 * {2}^{(\frac{e^{2}}{x^{2}})}e^{2}ln(2)}{x^{4}} + \frac{4 * {2}^{(\frac{e^{2}}{x^{2}})}e^{4}ln^{2}(2)}{x^{6}}\\ \end{split}\end{equation} \]





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