Embibe Experts Solutions for Chapter: Differential Coefficient, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

If $e^{\theta \varphi }=c+4\theta \varphi ,$ where $c$ is an arbitrary constant and $\varphi$ is a function of $\theta ,$ then what is $\varphi d\theta$ equal to?

If $x^m{y}^n=a^{m+n},$ then what is $\frac{dy}{dx}$ equal to?

What is the derivative of ${\tan }^{-1}x$ with respect to ${\cot }^{-1}x?$

What is the derivative of $2^{(\sin x{)}^2}$ with respect to $\sin x?$

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

If $f\left(x\right)=\sin \left(\cos x\right),$ then $f\text{'}\left(x\right)$ is equal to