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Question
Find the second order derivatives of the following function log (sin x) ?
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Solution
\[y = \log\left( \sin x \right)\]
\[\text { Differentiating w . r . t . x, we get }\]
\[\frac{d y}{d x} = \frac{1}{\sin x} \times \cos x = \cot x\]
\[\text { Differentiating again w . r . t . x, we get }\]
\[\frac{d^2 y}{d x^2} = - {cosec}^2 \ x\]
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