Amit M Agarwal Solutions for Chapter: Differentiation, Exercise 2: Target Exercise 2.2

The differential coefficient of $f\left({\log }_{e}x\right)$ w.r.t. $x,$ where $f\left(x\right)={\log }_{e}x$, is:

If $f\left(x\right)={\log }_e\left|x\right|, x\ne 0,$ then $f^{\text{'}}\left(x\right)$ is equals to

Let $f\left(x\right)=\sin x, g\left(x\right)=x^2$ and $h\left(x\right)={\log }_{e}x$. If $F\left(x\right)=h\left(f\left(g\left(x\right)\right)\right)$, then $F^{\text{'}}\left(x\right)$ is

If $f\left(x\right)=\cos x\cos 2x\cos 4x\cos 8x\cos 16x$, then $f\text{'}\left(\frac{\pi }{4}\right)$ is

If $y=f\left(\frac{3x+4}{5x+6}\right)$ and $f^{\text{'}}\left(x\right)=\tan x^2$, then $\frac{dy}{dx}$ is equal to

If $y=\left|\cos x\right|+\left|\sin x\right|$, then $\frac{dy}{dx}$ at $x=\frac{2\pi }{3}$ is

If $f^{\text{'}}\left(x\right)=\sin x+\sin 4x.\cos x,$ then $f^{\text{'}}\left(2x^2+\frac{\pi }{2}\right)$ is

If $f^{\text{'}}\left(x\right)=\sqrt{2x^2-1}$ and $y=f\left(x^2\right),$ then $\frac{dy}{dx}$ at $x=-1,$ is