G Tewani Solutions for Chapter: Methods of Differentiation, Exercise 2: DPP

The derivative of the function represented parametrically as $x=2t-\left|t\right|, y=t^3+t^2\left|t\right|$ at $t=0$ is

If $y={\tan }^{-1}\frac{u}{\sqrt{1-u^2}}$ and $x={\sec }^{-1}\frac{1}{2u^2-1}$, where $u\in \left(0,\frac{1}{\sqrt{2}}\right)\cup \left(\frac{1}{\sqrt{2}},1\right)$, then the value of  $2\frac{dy}{dx}+1$ is

The differential coefficient of ${\sin }^{-1}\left(\frac{4\sin 2x+3\cos 2x}{5}\right)$ with respect to ${\cos }^{-1}\left(\frac{5\cos x-4\sin x}{\sqrt{41}}\right)$ is:

If $xy={\left(x+y\right)}^n$ and $\frac{dy}{dx}=\frac{y}{x}$, then $n=$

If $x+y=3e^2$, then $\frac{d}{dx}\left(x^y\right)=0$ for $x=$

If $f\left(x\right)=(x-1{)}^{100}(x-2{)}^{2\left(99\right)}$$(x-3{)}^{3\left(98\right)}\dots (x-100{)}^{100},$ then the value of $\frac{f^{\text{'}}\left(101\right)}{f\left(101\right)}$ is

A curve in the $xy$-plane is parametrically given by $x=t+t^3$ and $y=t^2,$ where $t\in R$ is the parameter. Then, the value(s) of $t$ for which $\frac{dy}{dx}=\frac{1}{2}$ is

If $y=x^{(\log x{)}^{\log \left(\log \left(x\right)\right)}}$, then $\frac{dy}{dx}$ is