If xy_e(x+y) = 1, then dy/dx = Option 1: -(1/x^2+y/x+y)(y/x+y+_e(x+y)) Option 2: -(x+y+x^2y)/x^2[y+(x+y)_e(x+y)] Option 3: (1/x^2+y/x+y)(y/x+y+_e(x+y)) Option 4: (x+y+x^2y)/x^2[y+(x+y)_e(x+y)]

The answer is '-(x+y+x^2y)/x^2[y+(x+y)_e(x+y)]'. View full solution:

CUET Mathematics - If xy_e(x+y) = 1, then dy/dx = | PYQs + Solutions

CUET Mathematics 2026 26th May Shift 2

Calculus

Hard

common

$-\left(\dfrac{1}{x^2}+\dfrac{y}{x+y}\right)\left(\dfrac{y}{x+y}+\log_e(x+y)\right)$

$\dfrac{-(x+y+x^2y)}{x^2[y+(x+y)\log_e(x+y)]}$

$\left(\dfrac{1}{x^2}+\dfrac{y}{x+y}\right)\left(\dfrac{y}{x+y}+\log_e(x+y)\right)$

$\dfrac{(x+y+x^2y)}{x^2[y+(x+y)\log_e(x+y)]}$

✅ Correct Option: 2

Related questions:

12th May Shift 2

If $y=7^x\log(5x^3)$ , then $\dfrac{dy}{dx}$ is equal to: (consider $\log_e x = \log x$ )

23 May Shift 3

If $y = x^x$ , $\frac{dy}{dx}$ will be:

22 May Shift 2

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) $\mathbb{R} - \{n\pi: n \in \mathbb{Z}\}$
(D) $x^{-n}, n \in \mathbb{N}$ is continuous on:	(IV) $\mathbb{R} - \left\{(2n + 1)\frac{\pi}{2}: n \in \mathbb{Z}\right\}$

Choose the correct answer from the options given below: