Q10  Find the second order derivatives of the functions given in Exercises 1 to 10. 

         \sin (\log x )

Answers (1)

Given function is
y = \sin(\log x)
Now, differentiation w.r.t. x
\frac{dy}{dx}=\frac{d(\sin(\log x))}{dx}=\cos (\log x).\frac{1}{x}= \frac{\cos (\log x)}{x}
Now, second order derivative is 
Using Quotient rule
\frac{d^2y}{dx^2}=\frac{-\sin(\log x)\frac{1}{x}.x-\cos(\log x).1}{x^2} = \frac{-(\sin (\log x)+\cos(\log x))}{x^2}
Therefore,  second order derivative is \frac{d^2y}{dx^2} = \frac{-(\sin (\log x)+\cos(\log x))}{x^2}

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