Question
Find the second order derivatives of the function given in Exercise:
$\sin(\log\text{x})$
$\sin(\log\text{x})$
$\therefore\ \frac{\text{d}^2\text{y}}{\text{dx}^{2}}=\cos(\log\text{x}).\frac{\text{d}}{\text{dx}}\Big(\frac{1}{\text{x}}\Big)+\frac{1}{\text{x}}.\frac{\text{d}}{\text{dx}}[\cos(\log\text{x})]$
$=\cos(\log\text{x}).\Big(-\frac{1}{\text{x}^2}\Big)+\frac{1}{\text{x}}.\Big[\frac{-\sin(\log\text{x})}{\text{x}}\Big]$ $=-\frac{\cos(\log\text{x})}{\text{x}^2}-\frac{\sin(\log\text{x})}{\text{x}^2}=-\frac{1}{\text{x}^2}[\cos(\log\text{x})+\sin(\log\text{x})]$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\begin{bmatrix}\text{x}+10&\text{y}^2+2\text{y}\\0&-4\end{bmatrix}=\begin{bmatrix}3\text{x}+4&3\\0&\text{y}^2-5\text{y}\end{bmatrix}$