Embibe Experts Solutions for Chapter: Differentiation, Exercise 1: TS EAMCET - 5 August 2021 Shift 2

If $y={\cos }^{-1}\left(\tan hx\right)+\sin h\left(\sin 6x\right),$ then $\frac{dy}{dx}=$

If $\left(a+bx\right)e^{\frac{y}{x}}=x$, then $\frac{d^{2}y}{d{x}^2}=$

If $f\left(x\right)=\frac{{\cos }^{2}x}{1+{\sin }^{2}x}$, then $f\left(\frac{\pi }{4}\right)-3f^{\text{'}}\left(\frac{\pi }{4}\right)=$

If $x{e}^{xy}=y+{\sin }^{2}x,$ then $\frac{dy}{dx}$ at $x=0$ is

The derivate of $(\log x{)}^{\sin x}$ with respect to $\cos x$ at $x=\frac{\pi }{2}$ is

If $f\left(x\right)=-\left({\sin }^{2}x+{\cos }^{5}x\right),$ then $\underset{x\to 0}{\lim }\frac{1}{x}{f}^{\text{'}}\left(x\right)$

If $y=x^{\sqrt{x}},$ then $\frac{dy}{dx}=$

If $x=a(t-\sin t)$ and $y=a(1+\cos t)$ then $\frac{d^{2}y}{d{x}^2}=$