Question

Find the second order derivative of the given functions.

sin (log x)

Answer 1

Let y = sin (log x)

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

$\frac{dy}{dx}=cos\left(logx\right)\frac{d}{dx}\left(logx\right)=cos\left(logx\right)\frac{1}{x}=\frac{cos\left(logx\right)}{x}and\frac{d^{2}y}{d{x}^2}=\frac{d}{dx}\left(\frac{cos\left(logx\right)}{x}\right)=\frac{x\frac{d}{dx}\left(cos\right(logx\left)\right)-cos\left(logx\right)\frac{d}{dx}\left(x\right)}{x^2}\frac{x\{-sin(logx).\frac{1}{x}\}-cos\left(logx\right).1}{x^2}\left(Usingquotientrule\right)=-\frac{sin\left(logx\right)+cos\left(logx\right)}{x^2}$