If y = ^-1x, then (1-x^2)d^2y/dx^2 is equal to Option 1: -xdy/dx Option 2: xdy/dx Option 3: y/xdy/dx Option 4: -y/xdy/dx

The answer is 'xdy/dx'. View full solution:

Calculus > Continuity & Differentiability

Medium

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If $y = \sin^{-1}x$, then $(1-x^2)\frac{d^2y}{dx^2}$ is equal to

$-x\frac{dy}{dx}$

$x\frac{dy}{dx}$

$\frac{y}{x}\frac{dy}{dx}$

$-\frac{y}{x}\frac{dy}{dx}$

✅ Correct Option: 2

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If $x^2 - y^2 = 1$ , then which of the following is correct?

(A) $(x^2 - 1)\left(\frac{dy}{dx}\right)^2 = x^2$

(B) $(x^2 - 1)\left(\frac{d^2y}{dx^2}\right)^2 = x^2$

(D) $(x^2 - 1)^3\left(\frac{d^2y}{dx^2}\right)^2 = 1$

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Match List-I with List-II

Where $\mathbb{R}$ is set of real numbers

List-I	List-II
(A) $\sin x$ is continuous on:	(I) $\mathbb{R} - \{0\}$
(B) $\tan x$ is continuous on:	(II) $\mathbb{R}$
(C) $\cot x$ is continuous on:	(III) $\mathbb{R} - \{n\pi: n \in \mathbb{Z}\}$
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Match the LIST-I with LIST-II

LIST-I (Function in parametric form)	LIST-II ( $\dfrac{dy}{dx}=$ )
A. $x=t, y=t$	I. 1
B. $x=t^2, y=2t$	II. $\dfrac{1}{t}$
C. $x=3t, y=t^2$	III. $\dfrac{2t}{3}$
D. $x=2t, y=3t^2$	IV. $3t$

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