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Find the Second Order Derivatives of the Following Function Log (Sin X) ? - Mathematics

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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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Chapter 12: Higher Order Derivatives - Exercise 12.1 [Page 16]

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RD Sharma Mathematics [English] Class 12
Chapter 12 Higher Order Derivatives
Exercise 12.1 | Q 1.3 | Page 16

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