Maharashtra Board Solutions for Chapter: Diffrentiation, Exercise 3: MISCELLANEOUS EXERCISE

If $y=\frac{x-4}{\sqrt{x+2}}$, then $\frac{dy}{dx}$

If $y=\frac{ax+b}{cx+d}$, then $\frac{dy}{dx}=$

Discuss whether the function $f\left(x\right)=|x+1|+|x-1|$ is differentiable $\forall x\in \mathbf{R}$

Test whether the function $f\left(x\right)=\left\{\begin{array}{l}2x-3, \mathrm{for} x\ge 2\\ x-1, \mathrm{for} x<2\end{array}\right.$ is differentiable at $x=2$.

Test whether the function $f\left(x\right)=\left\{\begin{array}{lc}{x}^2+1,& \text{ for }x\ge 2\\ 2x+1,& \text{ for }x<2\end{array}\right.$ is differentiable at $x=2$.

Test whether the function $f\left(x\right)=\left\{\begin{array}{lc}5x-3x^2,& \text{ for }x\ge 1\\ 3-x,& \text{ for }x<1\end{array}\right.$ is differentiable at $x=1$

If $f\left(2\right)=4,f^{\text{'}}\left(2\right)=1$ then find $\underset{x\to 2}{\lim }\left[\frac{xf\left(2\right)-2f\left(x\right)}{x-2}\right]$

If $y=\frac{e^x}{\sqrt{x}}, \text{and} \frac{dy}{dx}=\frac{e}{k}$ when $x=1$ then find the value of $k$.