Embibe Experts Solutions for Chapter: Continuity and Differentiability, Exercise 1: Haryana Board-2019

Differentiate $\sin \left(x^2+5\right)$ w.r.t $x$.

Find $\frac{dy}{dx}$ from the equation $2x+3y=\sin y$.

If $x=2a{t}^2,y=a{t}^4$, then find $\frac{dy}{dx}$.

Find the value of $k$ so that the function $f$ defined by $f\left(x\right)=\left\{\begin{array}{cc}\frac{k \cos x}{\pi -2x},& \mathrm{if} x\ne \frac{\pi }{2}\\ 3,& \mathrm{if} x=\frac{\pi }{2}\end{array}\right.$ is continuous at $x=\frac{\pi }{2}$

Differentiate $\sec \left(\tan \sqrt{x}\right)$ with respect to $x$.

Find out whether the following function is continuous or not at $x=2$ :​

$f\left(x\right)=x^3-3, x\le 2$

       $=x^2+1, x>2$​​​​​​

If $x=a(\cos \theta +\theta \sin \theta )$ and $y=a(\sin \theta -\theta \cos \theta )$, then find $\frac{dy}{dx}$, at $\theta =\frac{\pi }{4}$.

If $y=(\sin x{)}^{\sin x},0<x<\pi$, find $\frac{dy}{dx}$.