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Questions › CUET-PG › CUET-PG 2026 › Q72
4 marks, −1Mathematics › Multivariable calculus › Partial derivatives and differentiabilityHardabout 1 min

CUET-PG 2026 Question 72: Multivariable calculus

Match the partial derivative of function Z=x2+xy2+yZ = x^2 + xy^2 + yZ=x2+xy2+y.

List I

A. ZxZ_xZx​

B. ZyZ_yZy​

C. ZxyZ_{xy}Zxy​

D. ZyxZ_{yx}Zyx​.

List II

I. 2y

II. 2yx+12yx + 12yx+1

III. 2x+y22x + y^22x+y2

IV. 2y.

Choose the correct answer from the options given below:

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Plain-text version

Match the partial derivative of function Z = x² + xy² + y. List I A. Zₓ B. Z_y C. Z_(xy) D. Z_(yx). List II I. 2y II. 2yx + 1 III. 2x + y² IV. 2y. Choose the correct answer from the options given below: (A) A-I, B-III, C-II, D-IV (B) A-III, B-II, C-I, D-IV (C) A-II, B-III, C-I, D-IV (D) A-I, B-II, C-III, D-IV

Also written as: Match the partial derivative of function Z = x^2 + xy^2 + y. List I A. Z_x B. Z_y C. Z_(xy) D. Z_(yx). List II I. 2y II. 2yx + 1 III. 2x + y^2 IV. 2y. Choose the correct answer from the options given below:

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
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