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Questions › CUET-PG › CUET-PG 2023 Shift 1 › Q96
4 marks, −1Mathematics › Limits, continuity and differentiability › Implicit, logarithmic and higher-order differentiationHardabout 2 min

CUET-PG 2023 Shift 1 Question 96: Limits, continuity and differentiability

Find dydx\frac{dy}{dx}dxdy​ if x1+y+y1+x=0x\sqrt{1+y} + y\sqrt{1+x} = 0x1+y​+y1+x​=0.

  1. −1(1+x)2\frac{-1}{(1+x)^2}(1+x)2−1​
  2. 2(1+x)\frac{2}{(1+x)}(1+x)2​
  3. −11+x\frac{-1}{\sqrt{1+x}}1+x​−1​
  4. 1+x1+y\frac{1+x}{1+y}1+y1+x​

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Plain-text version

Find dy/dx if x√(1+y) + y√(1+x) = 0. 1. (-1)/((1+x)²) 2. 2/((1+x)) 3. (-1)/(√(1+x)) 4. (1+x)/(1+y) (A) (-1)/((1+x)²) (B) 2/((1+x)) (C) (-1)/(√(1+x)) (D) (1+x)/(1+y)

Also written as: Find dy/dx if xsqrt(1+y) + ysqrt(1+x) = 0. 1. (-1)/((1+x)^2) 2. 2/((1+x)) 3. (-1)/(sqrt(1+x)) 4. (1+x)/(1+y)

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Implicit, logarithmic and higher-order differentiation, part of Limits, continuity and differentiability in Mathematics.

Differentiating relations that are not solved for y, and taking second and higher derivatives.

TestStop has 9 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q11Let x³ + 3y² = 4 for all x, y ∈ ℝ, y′ = dy/dx and y′′ = d²y/dx². Then
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Question from the CUET-PG 2023 Shift 1 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.