D.K. Ramesh Kumar and C. V. Jayanna Solutions for Chapter: Differentiation, Exercise 1: Exercise 1

If $y=tan{h}^{-1}(1+x)$ then $\frac{dy}{dx}=$.

If $x^2+xy+y^2=0$ then $\frac{dy}{dx}=$?

If $S=ta{n}^{-1}\sqrt{1+x^2}-\frac{1}{x}$ and $T=ta{n}^{-1}x$ then $\frac{dS}{dT}=$?

If $f\left(x\right)={\cos }^{-1}\left[\frac{1}{\sqrt{13}}(2\cos x-3\sin x)\right]$ then $f^{\text{'}}(0.5)=$

If $x=t^2$ and $y=t^3$ then $\frac{d^{2}y}{d{x}^2}=$

If $y=\cos \left(3{\cos }^{-1}x\right)+\cos \left(2{\cos }^{-1}x\right)\frac{dy}{dx}=$

If $y={\sin }^{-1}\left[\sqrt{1-x^2}\tan \left({\sin }^{-1}x\right)\right]$ then $\frac{dy}{dx}=$

If $x+y={\tan }^{-1}y$ and $\frac{d^{2}y}{d{x}^2}=f\left(y\right)\frac{dy}{dx}$ then $f\left(y\right)=$