There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (ln(\frac{sin(x)}{x})){\frac{1}{x}}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{ln(\frac{sin(x)}{x})}{x^{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{ln(\frac{sin(x)}{x})}{x^{2}}\right)}{dx}\\=&\frac{-2ln(\frac{sin(x)}{x})}{x^{3}} + \frac{(\frac{-sin(x)}{x^{2}} + \frac{cos(x)}{x})}{x^{2}(\frac{sin(x)}{x})}\\=&\frac{-2ln(\frac{sin(x)}{x})}{x^{3}} + \frac{cos(x)}{x^{2}sin(x)} - \frac{1}{x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2ln(\frac{sin(x)}{x})}{x^{3}} + \frac{cos(x)}{x^{2}sin(x)} - \frac{1}{x^{3}}\right)}{dx}\\=&\frac{-2*-3ln(\frac{sin(x)}{x})}{x^{4}} - \frac{2(\frac{-sin(x)}{x^{2}} + \frac{cos(x)}{x})}{x^{3}(\frac{sin(x)}{x})} + \frac{-2cos(x)}{x^{3}sin(x)} + \frac{-cos(x)cos(x)}{x^{2}sin^{2}(x)} + \frac{-sin(x)}{x^{2}sin(x)} - \frac{-3}{x^{4}}\\=&\frac{6ln(\frac{sin(x)}{x})}{x^{4}} - \frac{4cos(x)}{x^{3}sin(x)} - \frac{cos^{2}(x)}{x^{2}sin^{2}(x)} + \frac{5}{x^{4}} - \frac{1}{x^{2}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !