The differential coefficient of {cos ^{ - 1}} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $y = {\cos ^{ - 1}}(\sqrt x )$ and $z = \sqrt {1 - x} $. First,differentiate $y$ with respect to $x$: $\frac{dy}{dx} = -\frac{1}{\sqrt{1 - (\s

Vedclass · Accepted Answer

$\frac{1}{\sqrt x }$

Vedclass · Answer

(C) Let $y = {\cos ^{ - 1}}(\sqrt x )$ and $z = \sqrt {1 - x} $. First,differentiate $y$ with respect to $x$: $\frac{dy}{dx} = -\frac{1}{\sqrt{1 - (\sqrt{x})^2}} 	imes \frac{d}{dx}(\sqrt{x}) = -\frac{1}{\sqrt{1 - x}} 	imes \frac{1}{2\sqrt{x}}$. Next,differentiate $z$ with respect to $x$: $\frac{dz}{dx} = \frac{1}{2\sqrt{1 - x}} 	imes \frac{d}{dx}(1 - x) = \frac{1}{2\sqrt{1 - x}} 	imes (-1) = -\frac{1}{2\sqrt{1 - x}}$. Now,find the differential coefficient of $y$ with respect to $z$: $\frac{dy}{dz} = \frac{dy/dx}{dz/dx} = \frac{-\frac{1}{\sqrt{1 - x}} 	imes \frac{1}{2\sqrt{x}}}{-\frac{1}{2\sqrt{1 - x}}} = \frac{1}{\sqrt{x}}$. Thus,the correct option is $C$.

The differential coefficient of ${\cos ^{ - 1}}(\sqrt x )$ with respect to $\sqrt {1 - x} $ is

Similar Questions

If $x=3 \tan t$ and $y=3 \sec t$,then the value of $\frac{d^2 y}{d x^2}$ at $t=\frac{\pi}{4}$ is

If $\sin y = \sin 3t$ and $x = \sin t$, then $\frac{dy}{dx} = $

If $x=f(\theta)$ and $y=g(\theta)$,then $\frac{d^2 y}{d x^2}=$

If $x = a \cos \theta$ and $y = a \sin \theta$, then $\frac{d^2 y}{d x^2} = \rule{1cm}{0.15mm} \, (a \neq 0; \theta \neq k\pi, k \in Z)$.

$x=\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), y=\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right) \Rightarrow \frac{d y}{d x}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module