Amit M Agarwal Solutions for Chapter: Differentiation, Exercise 7: Proficiency in 'Differentiation' Exercise 1

If $f\left(x\right)=x^n$, $n\in N$ then the value of $f\left(1\right)-\frac{f^{\text{'}}\left(1\right)}{1!}+\frac{f^{\text{'}\text{'}}\left(1\right)}{2!}-\frac{f^{\text{'}\text{'}\text{'}}\left(1\right)}{3!}+\frac{f^{\left(iv\right)}\left(1\right)}{4!}-\dots \dots +\frac{{\left(-1\right)}^n{f}^n\left(1\right)}{n!}$is:

If $\mathrm{y}={\mathrm{x}}^{{\left(\mathrm{lnx}\right)}^{\ln \left(\mathrm{lnx}\right)}}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is/are equal to:

Which of the following functions are not derivable at $x=0$?

Let $f\left(x\right)=\frac{\sqrt{x-2\sqrt{x-1}}}{\sqrt{x-1}-1}·x$, then

If $2^x+2^y=2^{x+y}$, then $\frac{dy}{dx}$ is equal to:

For the function $y=f\left(x\right)=\left(x^2+bx+c\right)e^x$, which of the following holds true?

If $\sqrt{y+x}+\sqrt{y-x}=c$ (where $c\ne 0$), then $\frac{dy}{dx}$ has the value equal to:

If $y=\mathrm{t}\mathrm{a}\mathrm{n}x\mathrm{t}\mathrm{a}\mathrm{n}2x\mathrm{t}\mathrm{a}\mathrm{n}3x$, then $\frac{dy}{dx}$ is equal to: