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Questions › DSE › DSE 2020 › Q34
4 marks, −1Mathematics › Multivariable calculus › Partial derivatives and differentiabilityHardabout 4 min

DSE 2020 Question 34: Multivariable calculus

If f:R2→Rf:\mathbb{R}^2\to\mathbb{R}f:R2→R is given by f(x,y)=xyx2+y2f(x,y)=\dfrac{xy}{x^2+y^2}f(x,y)=x2+y2xy​ for (x,y)≠(0,0)(x,y)\ne(0,0)(x,y)=(0,0) and f(0,0)=0f(0,0)=0f(0,0)=0, then

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If f:ℝ²→ℝ is given by f(x,y)=xy/(x²+y²) for (x,y)≠(0,0) and f(0,0)=0, then (A) f is differentiable at (0,0) and both partial derivatives at (0,0) are 0 (B) f is non-differentiable at (0,0) and both partial derivatives at (0,0) are 0 (C) f is differentiable at (0,0) and neither partial derivative at (0,0) is 0 (D) f is non-differentiable at (0,0) and neither partial derivative at (0,0) exists

Also written as: If f:R^2->R is given by f(x,y)=xy/(x^2+y^2) for (x,y)!=(0,0) and f(0,0)=0, then

Multivariable calculus has come up 32 times in 7 exams since 2007.

What this question tests

This question is on Partial derivatives and differentiability, part of Multivariable calculus in Mathematics.

Derivatives with respect to one variable at a time, and how they relate to continuity and differentiability.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q19Let f:ℝ²→ℝ be f(x,y) = (x y²)/(x³ + 2x² y + y³) with f(0,0)=0. Then
Practise Multivariable calculusMore on Partial derivatives and differentiability

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.