Category: Differentiation

Question Number 44267 by rahul 19 last updated on 25/Sep/18 $$Ifxϵ(\frac{1}{\sqrt{2}},1),differentiate{\cos }^{-1}\left(2x\sqrt{1-x^2}\right).$$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Sep/18 $$x=cos\alpha dx=-sin\alpha d\alpha$$$${y}={cos}^{−\mathrm{1}}…

Question Number 44209 by Tinkutara last updated on 23/Sep/18 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 175275 by mnjuly1970 last updated on 25/Aug/22 Answered by Rasheed.Sindhi last updated on 25/Aug/22 $$(-5,x+2y)\cup (2x-y-4,3)$$$$=(-5,a)\cup (a,3)$$$$a=x+2y=2x-y-4=\frac{-5+3}{2}=-1$$$$a=-1$$$${x}+\mathrm{2}{y}=−\mathrm{1}\:\wedge\:\mathrm{2}{x}−{y}−\mathrm{4}=−\mathrm{1}…

Question Number 109724 by bobhans last updated on 25/Aug/20 $$y=\sqrt{x+\sqrt{x+\sqrt{x}}}\Rightarrow \frac{dy}{dx}?$$ Answered by ajfour last updated on 25/Aug/20 $${(y^2-x)}^2=x+\sqrt{x}$$$$\mathrm{2}\left({y}^{\mathrm{2}} −{x}\right)\left(\mathrm{2}{y}\frac{{dy}}{{dx}}−\mathrm{1}\right)=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}…

Question Number 44120 by peter frank last updated on 21/Sep/18 Answered by ajfour last updated on 21/Sep/18 $$\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }=\frac{a\sin \theta }{a+a\cos \theta }=\frac{\sin \theta }{1+\cos \theta }$$$$\frac{d^{2}y}{{dx}^2}=\left[\frac{d}{d\theta }\left(\frac{dy}{dx}\right)\right]/\left(\frac{dx}{d\theta }\right)$$$$\:\:\:=\frac{\mathrm{cos}\:\theta\left(\mathrm{1}+\mathrm{cos}\:\theta\right)−\mathrm{sin}\:\theta\left(−\mathrm{sin}\:\theta\right)}{\left(\mathrm{1}+\mathrm{cos}\:\theta\right)^{\mathrm{2}} ×{a}\left(\mathrm{1}+\mathrm{cos}\:\theta\right)}…