Question

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

Answer 1

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

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

\[\frac{d y}{d x} = \cos\left( \log x \right) \times \frac{1}{x}\]

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

\[\frac{d^2 y}{d x^2} = - \sin\left( \log x \right)\frac{1}{x} \times \frac{1}{x} + \cos\left( \log x \right) \times \frac{- 1}{x^2}\]

\[ = \frac{- \left[ \sin\left( \log x \right) + \cos\left( \log x \right) \right]}{x^2}\]