Embibe Experts Solutions for Exercise 2: EXERCISE 5.3

The set of points, where the function $f\left(x\right)=x\left|x\right|$ is differentiable, is

The number of points where $f\left(x\right)=\left|x^2-3x+2\right|$ is non-differentiable is

If $\left[·\right]$ represents greatest integer function, then the left-hand derivative of $f\left(x\right)=\left[x\right]\sin \pi x$ at $x=k,k$ is an integer, is given by

If $f\left(x\right)=\left|x-2020\right|$, then $f\text{'}\left(x\right)$ at $x=2019$,is given by

The values of $a$and $b$, so that the function $f\left(x\right)=\left\{\begin{array}{cl}\left(x^2+3x+a\right);& \mathrm{when} x\le 1\\ (bx+2);& \mathrm{when} x>1\end{array};\right.$ is differentiable for each $x\in R;$ are respectively

Show that the function$f\left(x\right)=\left\{\begin{array}{cl}x\sin \left(\frac{1}{x}\right)& \mathrm{when} x\ne 0\\ 0& \mathrm{when} x=0\end{array}\right.$, is continuous but not differentiable at $x=0$.

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

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