There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ 14 + \frac{19x}{6} - {x}^{2} - \frac{{x}^{3}}{6}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{19}{6}x - x^{2} - \frac{1}{6}x^{3} + 14\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{19}{6}x - x^{2} - \frac{1}{6}x^{3} + 14\right)}{dx}\\=&\frac{19}{6} - 2x - \frac{1}{6}*3x^{2} + 0\\=& - 2x - \frac{x^{2}}{2} + \frac{19}{6}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 2x - \frac{x^{2}}{2} + \frac{19}{6}\right)}{dx}\\=& - 2 - \frac{2x}{2} + 0\\=& - x - 2\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - x - 2\right)}{dx}\\=& - 1 + 0\\=& - 1\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !