If x=sqrt{1-tan y}, then frac{dy}{dx}= | vedclass

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

Question

(B) Given $x = \sqrt{1-	an y}$.Squaring both sides, we get $x^2 = 1 - 	an y$.Rearranging the terms, $	an y = 1 - x^2$.Now, differentiate both sides

Vedclass · Accepted Answer

$-\frac{2x}{x^4-2x^2+2}$

Vedclass · Answer

(B) Given $x = \sqrt{1-	an y}$.Squaring both sides, we get $x^2 = 1 - 	an y$.Rearranging the terms, $	an y = 1 - x^2$.Now, differentiate both sides with respect to $x$:$\frac{d}{dx}(	an y) = \frac{d}{dx}(1 - x^2)$.Using the chain rule, $\sec^2 y \cdot \frac{dy}{dx} = -2x$.We know that $\sec^2 y = 1 + 	an^2 y$.Substitute $	an y = 1 - x^2$ into the expression:$\sec^2 y = 1 + (1 - x^2)^2 = 1 + (1 - 2x^2 + x^4) = x^4 - 2x^2 + 2$.Now, substitute this back into the derivative equation:$(x^4 - 2x^2 + 2) \cdot \frac{dy}{dx} = -2x$.Therefore, $\frac{dy}{dx} = -\frac{2x}{x^4 - 2x^2 + 2}$.

If $x=\sqrt{1-\tan y}$, then $\frac{dy}{dx}=$

Similar Questions

If $\sin(xy) + \cos(xy) = 0$,then $\frac{dy}{dx} = $

If $x \sqrt{1+y}+y \sqrt{1+x}=0$,then $\frac{d y}{d x}$ is equal to

If $y = \log_y x$,then $\frac{dy}{dx}$ is equal to

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

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module