Question

Find \[\frac{d^2 y}{d x^2}\] where \[y = \log \left( \frac{x^2}{e^2} \right)\] ?

Answer 1

Here,

\[y = \log\left( \frac{x^2}{e^2} \right)\] 

\[\text { Differentiating  w . r . t .   x,   we  get }\] 

\[\frac{d y}{d x} = \frac{1}{\frac{x^2}{e^2}} \times \frac{2x}{e^2} = \frac{2}{x}\] 

\[\text { Differentiating  again  w . r . t .   x,   we  get }\] 

\[\frac{d^2 y}{d x^2} = \frac{- 2}{x^2}\] ?