Embibe Experts Solutions for Chapter: Differential Coefficient, Exercise 1: CUSAT CAT 2017

If $y={\cos }^{-1}\left(\cos x\right)$, then $y^{\text{'}}\left(x\right)=$

If $y=\underset{n\to \infty }{\lim }\left(1+x\right)\left(1+x^2\right)\left(1+x^4\right)...\left(1+x^{2n}\right)$, and $x^2<1$, then $y^{\text{'}}$ is equal to

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

If $\sin y=x\sin \left(a+y\right)$, then $\frac{dy}{dx}$ is

If $y=\frac{x+c}{1+x^2}$ where $c$ is a constant, when $y$ is stationary, $xy$ is equal to -

If $x^2+y^2=t-\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then $\frac{dy}{dx}=$

The second order derivative $\frac{d^{2}y}{d{x}^2}$ at $t=\frac{\pi }{4}$ where $x=a{\sin }^{3}t$ and $y=a{\cos }^{3}t$ is