Question

If $y=\log \left(\log x\right)$ then $\frac{d^{2}y}{d{x}^2}$ is equal to

• A. $\frac{-(1+\log x)}{(x\log x{)}^2}$
• B. $\frac{-(1+\log x)}{\left(x^2\log x\right)}$
• C. $\frac{(1+\log x)}{(x\log x{)}^2}$
• D. $\frac{(1+\log x)}{\left(x^2\log x\right)}$

Answer 1

The correct option is A $\frac{-(1+\log x)}{(x\log x{)}^2}$

$y=\log \left(\log x\right)\frac{dy}{dx}=\frac{1}{\log x}\times \frac{1}{x}=\frac{1}{x\log x}\Rightarrow \frac{d^{2}y}{d{x}^2}=\frac{-(1+\log x)}{(x\log x{)}^2}$