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

Answer: 1/((x+1)^2). Solution: From e^y(x+1)=1, take logs: y = -_e(x+1). Then dy/dx = -1/(x+1) and differentiating again, d^2y/dx^2 = 1/((x+1)^2).

Calculus

Continuity & Differentiability

Easy

common

If $e^y(x+1) = 1$ , then $\dfrac{d^2y}{dx^2}$ is equal to

$\dfrac{-1}{x+1}$

$\dfrac{-1}{(x+1)^2}$

$\dfrac{1}{x+1}$

$\dfrac{1}{(x+1)^2}$

✅ Correct Option: 4

From $e^y(x+1)=1$ , take logs: $y = -\log_e(x+1)$ .

Then $\dfrac{dy}{dx} = -\dfrac{1}{x+1}$ and differentiating again, $\dfrac{d^2y}{dx^2} = \dfrac{1}{(x+1)^2}$ .

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Match List - I with List - II.

	List - I		List - II
(A)	$y = \log(\sin x)$	(I)	$\frac{d^2y}{dx^2} = -\frac{1}{x^2}$
(B)	$y = e^{(1 + \log x)}$	(II)	$\frac{d^2y}{dx^2} = 2$
(C)	$y = \log\lvert x \rvert$	(III)	$\frac{d^2y}{dx^2} = 0$
(D)	$y = x^2 + 4x - 1$	(IV)	$\frac{d^2y}{dx^2} = -\csc^2 x$

Choose the correct answer from the options given below :

If ey(x+1)=1e^y(x+1) = 1ey(x+1)=1, then d2ydx2\dfrac{d^2y}{dx^2}dx2d2y​ is equal to

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CUET Mathematics Past Year Questions (Topic-Wise)

If $e^y(x+1) = 1$ , then $\dfrac{d^2y}{dx^2}$ is equal to