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Questions › GATE › GATE 2025 › Q31
1 mark, −0.333Mathematics › Multivariable calculus › Homogeneous functions and Euler's theoremModerateabout 1 min

GATE 2025 Question 31: Multivariable calculus

Let f(x,y,z)=x2y3zf(x,y,z) = x^2 y^3 zf(x,y,z)=x2y3z. Then, x∂f∂x(x,y,z)+y∂f∂y(x,y,z)+z∂f∂z(x,y,z)=x\dfrac{\partial f}{\partial x}(x,y,z) + y\dfrac{\partial f}{\partial y}(x,y,z) + z\dfrac{\partial f}{\partial z}(x,y,z) =x∂x∂f​(x,y,z)+y∂y∂f​(x,y,z)+z∂z∂f​(x,y,z)=

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Plain-text version

Let f(x,y,z) = x² y³ z. Then, x(∂ f)/(∂ x)(x,y,z) + y(∂ f)/(∂ y)(x,y,z) + z(∂ f)/(∂ z)(x,y,z) = (A) f(x,y,z) (B) 2f(x,y,z) (C) 3f(x,y,z) (D) 6f(x,y,z)

Also written as: Let f(x,y,z) = x^2 y^3 z. Then, x(d f)/(d x)(x,y,z) + y(d f)/(d y)(x,y,z) + z(d f)/(d z)(x,y,z) =

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

What this question tests

This question is on Homogeneous functions and Euler's theorem, part of Multivariable calculus in Mathematics.

Functions that scale in a fixed way when all inputs scale, and the identity this gives.

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

  • IIT JAM 2022 · Q38Which of the following functions is/are homogeneous?
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Question from the GATE 2025 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.