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