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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (x - 1)log_{3}^{x} + e^{3}x\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = xlog_{3}^{x} - log_{3}^{x} + xe^{3}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( xlog_{3}^{x} - log_{3}^{x} + xe^{3}\right)}{dx}\\=&log_{3}^{x} + x(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))}) - (\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))}) + e^{3} + xe^{3}*0\\=&log_{3}^{x} + \frac{1}{ln(3)} - \frac{1}{xln(3)} + e^{3}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( log_{3}^{x} + \frac{1}{ln(3)} - \frac{1}{xln(3)} + e^{3}\right)}{dx}\\=&(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))}) + \frac{-0}{ln^{2}(3)(3)} - \frac{-1}{x^{2}ln(3)} - \frac{-0}{xln^{2}(3)(3)} + e^{3}*0\\=&\frac{1}{xln(3)} + \frac{1}{x^{2}ln(3)}\\ \end{split}\end{equation} \]





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