Subject Experts Solutions for Chapter: Differentiation, Exercise 1: Practice Exercise

If $z=fof\left(x\right)$, where $f\left(x\right)=x^2$, then what is $\frac{dz}{dx}$ equal to?

What is the derivative of $\sqrt{\frac{1+\cos x}{1-\cos x}}?$

If $y=x\ln x+x{e}^x$, then what is the value of $\frac{dy}{dx}$ at $x=1?$

Eliminating the arbitrary constants $B$ and $C$ in the expression $y=\frac{2}{3C}{\left(Cx-1\right)}^{3/2}+B$, we get

What is the differential coefficient of $f\left(x\right)=\left\{\begin{array}{l} x^2-5, x\le 3\\ \sqrt{x+13}, x>3\end{array}\right.$ at $x=12?$

What is the derivative of ${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to ${\tan }^{-1}x?$

The derivative of $\ln \left(x+\sin x\right)$ with respect to $\left(x+\cos x\right)$ is

If $y={\cot }^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right]$, where $0<x<\frac{\pi }{2}$, then $\frac{dy}{dx}$ is equal to