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