There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {(1 + {x}^{2})}^{\frac{1}{3}}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{2} + 1)^{\frac{1}{3}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( (x^{2} + 1)^{\frac{1}{3}}\right)}{dx}\\=&(\frac{\frac{1}{3}(2x + 0)}{(x^{2} + 1)^{\frac{2}{3}}})\\=&\frac{2x}{3(x^{2} + 1)^{\frac{2}{3}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x}{3(x^{2} + 1)^{\frac{2}{3}}}\right)}{dx}\\=&\frac{2(\frac{\frac{-2}{3}(2x + 0)}{(x^{2} + 1)^{\frac{5}{3}}})x}{3} + \frac{2}{3(x^{2} + 1)^{\frac{2}{3}}}\\=&\frac{-8x^{2}}{9(x^{2} + 1)^{\frac{5}{3}}} + \frac{2}{3(x^{2} + 1)^{\frac{2}{3}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !