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

Answer: d^2y/dx^2 = (dy/dx)^2. Solution: From (x+1)e^y = 1: e^y = 1/(x+1), so y = -(x+1). dy/dx = -1/(x+1), so (dy/dx)^2 = 1/((x+1)^2). d^2y/dx^2 = 1/((x+1)^2). Therefore d^2y/dx^2 = (dy/dx)^2.

Applied Mathematics

Calculus

Medium

If $(x+ 1) e^y = 1$ , then :

$\frac{d^2y}{dx^2} = y^2$

$\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$

$\frac{d^2y}{dx^2} = -y^2$

$\frac{d^2y}{dx^2} = \frac{dy}{dx}$

✅ Correct Option: 2

From $(x+1)e^y = 1$ : $e^y = \frac{1}{x+1}$ , so $y = -\ln(x+1)$ .

$\frac{dy}{dx} = -\frac{1}{x+1}$ , so $\left(\frac{dy}{dx}\right)^2 = \frac{1}{(x+1)^2}$ .

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

Therefore $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$ .

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Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $(x+ 1) e^y = 1$ , then :