Question

Find the second order derivatives of the following function  log (log x)  ?

Answer 1

We have,

\[y = \log\left( \log x \right)\]
\[\text { Differentiating w . r . t . x, we get }\]
\[\frac{d y}{d x} = \frac{1}{\log x} \times \frac{1}{x} = \frac{1}{x\log x}\]
\[\text { Differentiating again w . r . t . x, we get }\]
\[\frac{d^2 y}{d x^2} = \frac{0 - \left( \log x + 1 \right)}{\left( x\log x \right)^2} = - \frac{\left( 1 + \log x \right)}{\left( x\log x \right)^2}\]