Question

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

Answer 1

\[y = \log\left( \sin x \right)\]

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

\[\frac{d y}{d x} = \frac{1}{\sin x} \times \cos x = \cot x\]

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

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