If y = frac{(sin^{-1} x)^2}{2}, then (1-x^2) | vedclass

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

Question

(C) Given, $y = \frac{(\sin^{-1} x)^2}{2}$.Differentiating with respect to $x$:$y_1 = \frac{d}{dx} \left[ \frac{(\sin^{-1} x)^2}{2} \right] = \frac{1}

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) Given, $y = \frac{(\sin^{-1} x)^2}{2}$.Differentiating with respect to $x$:$y_1 = \frac{d}{dx} \left[ \frac{(\sin^{-1} x)^2}{2} \right] = \frac{1}{2} \cdot 2(\sin^{-1} x) \cdot \frac{1}{\sqrt{1-x^2}} = \frac{\sin^{-1} x}{\sqrt{1-x^2}}$.Thus, $\sqrt{1-x^2} y_1 = \sin^{-1} x$.Differentiating again with respect to $x$ using the product rule:$\sqrt{1-x^2} y_2 + y_1 \cdot \frac{1}{2\sqrt{1-x^2}} (-2x) = \frac{1}{\sqrt{1-x^2}}$.Multiply both sides by $\sqrt{1-x^2}$:$(1-x^2) y_2 - x y_1 = 1$.

If $y = \frac{(\sin^{-1} x)^2}{2}$, then $(1-x^2) y_2 - x y_1 = $

Similar Questions

If $\frac{d^2x}{dy^2} \left( \frac{dy}{dx} \right)^3 + \frac{d^2y}{dx^2} = K$,then the value of $K$ is equal to

If $y = \sin(\log_e x)$, then $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx}$ is equal to

If $y=2 x^{n+1}+\frac{3}{x^{n}}$,then $x^{2} \frac{d^{2} y}{d x^{2}}$ is

Let $y = \frac{x^{2}}{(x+1)^{2}(x+2)}$. Then $\frac{d^{2} y}{dx^{2}}$ is

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$, then $\left(1+a^2 x^2\right)y''+2 a^2 x y'$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module