Embibe Experts Solutions for Chapter: Continuity and Differentiability, Exercise 1: CBSE-2018

If ${\left(x^2+y^2\right)}^2=xy$, find $\frac{dy}{dx}$.

If $x=a(2\theta -\sin 2\theta )\text{ and }y=a(1-\cos 2\theta )$, find $\frac{dy}{dx}$ when $\theta =\frac{\pi }{3}$.

If $y=\sin \left(\sin x\right)$, prove that $\frac{d^{2}y}{d{x}^2}+\tan x\frac{dy}{dx}+y{\cos }^{2}x=0$.

If $x^y-y^x=a^b$, find $\frac{dy}{dx}$.

If $y={\left({\sin }^{-1}x\right)}^2$, prove that $\left(1-x^2\right)\frac{d^{2}y}{d{x}^2}-x\frac{dy}{dx}-2=0$.

The greatest integer function defined by $f\left(x\right)=\left[x\right], 0<x<2$ is not differentiable at $x=$_____

If $x=a{t}^2,y=2at$, then find $\frac{d^{2}y}{d{x}^2}$.

If $y=e^{x^2\cos x}+(\cos x{)}^x$, then find $\frac{dy}{dx}$.