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Question

Find the second order derivative of the given functions.

sin (log x)


Solution

Let y = sin (log x)

Differentiating twicely w.r.t. x, we get

dydx=cos(log x)ddx(log x)=cos (log x)1x=cos(log x)xand d2ydx2=ddx(cos(log x)x)=xddx(cos(log x))cos(log x)ddx(x)x2x{sin(log x).1x}cos(log x).1x2  (Using quotient rule)=sin(log x)+cos (log x)x2

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