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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ 6{x}^{(\frac{4}{3})} - 3{x}^{\frac{1}{3}}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 6{x}^{\frac{4}{3}} - 3{x}^{\frac{1}{3}}\right)}{dx}\\=&6({x}^{\frac{4}{3}}((0)ln(x) + \frac{(\frac{4}{3})(1)}{(x)})) - 3({x}^{\frac{1}{3}}((0)ln(x) + \frac{(\frac{1}{3})(1)}{(x)}))\\=&8x^{\frac{1}{3}} - \frac{1}{x^{\frac{2}{3}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 8x^{\frac{1}{3}} - \frac{1}{x^{\frac{2}{3}}}\right)}{dx}\\=&\frac{8*\frac{1}{3}}{x^{\frac{2}{3}}} - \frac{\frac{-2}{3}}{x^{\frac{5}{3}}}\\=&\frac{8}{3x^{\frac{2}{3}}} + \frac{2}{3x^{\frac{5}{3}}}\\ \end{split}\end{equation} \]





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