Embibe Experts Solutions for Chapter: Differentiation, Exercise 1: MHT-CET 2019

If ${\log }_{10}\left(\frac{x^3-y^3}{x^3+y^3}\right)=2$, then $\frac{dx}{dy}=$

If $x^2+y^2=1,$ then $\frac{d^{2}x}{d{y}^2}=$

If $y={\tan }^{-1}\left(\sec x+\tan x\right)$, then $\frac{dy}{dx}=$

If $x=\mathrm{s}\mathrm{i}\mathrm{n}\theta , y={\mathrm{s}\mathrm{i}\mathrm{n}}^3\theta ,$ then $\frac{d^{2}y}{d{x}^2}$ at $\theta$ = $\frac{\pi }{2}$ is ….

If then $\mathrm{}{x}^y=e^{x-y},$ then $\frac{dy}{dx}$ at $x=1$ is ….

If $y=e^{4x}\cos 5x,$ then $\frac{d^{2}y}{d{x}^2}$ at $x=0$ is

If $y=3e^{5x}+5e^{3x}$, then $\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}=$

If $x=\log t, y+1=\frac{1}{t}$, then $e^{-x}\frac{d^{2}x}{d{y}^2}+\frac{dx}{dy}=$