There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {x}^{\frac{1}{3}}(x - 4)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{\frac{4}{3}} - 4x^{\frac{1}{3}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{\frac{4}{3}} - 4x^{\frac{1}{3}}\right)}{dx}\\=&\frac{4}{3}x^{\frac{1}{3}} - \frac{4*\frac{1}{3}}{x^{\frac{2}{3}}}\\=&\frac{4x^{\frac{1}{3}}}{3} - \frac{4}{3x^{\frac{2}{3}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x^{\frac{1}{3}}}{3} - \frac{4}{3x^{\frac{2}{3}}}\right)}{dx}\\=&\frac{4*\frac{1}{3}}{3x^{\frac{2}{3}}} - \frac{4*\frac{-2}{3}}{3x^{\frac{5}{3}}}\\=&\frac{4}{9x^{\frac{2}{3}}} + \frac{8}{9x^{\frac{5}{3}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !