Partial Derivatives Quizzes, Questions & Answers

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Top Trending Partial Derivatives Quizzes

Are you familiar with the mathematical rule, which wants that when all other variables are held constant, then the partial derivative rules for dealing with coefficients, simple powers of variables, constants, and sums/difference...

Questions: 10 | Attempts: 182 | Last updated: Mar 18, 2025

Sample Question 1
What's the particularity of the function f(x,y) = x^2(y)/ ((x^4) +( y^2))?

It is that it approaches "100" along any line through the origin.

It is that it approaches "1" along any line through the origin.

It is that it approaches "0" along any line through the origin.

It is that it approaches "-1" along any line through the origin.

Sample Question 2
What happens when the origin is approached along a parabola y=x^2?

It has a limit of 0.5

It has a limit of 1

It is negative

It is positive

Partial Derivatives Made Simple: Definitions, Tables & Mixed Partials

Partial derivatives reveal how multivariable functions change when one variable varies while the others remain fixed. This quiz deepens your understanding of first-order and higher-order partial derivatives, mixed partials, and...

Questions: 15 | Attempts: 11 | Last updated: Dec 17, 2025

Sample Question 1
For the function f(x,y) = 3x²y + 5xy³, find the partial derivative with respect to x.

6xy + 5y³

3x² + 15xy²

6xy + 15xy²

3x²*y + 5y³

Sample Question 2
Which statement correctly defines the partial derivative ∂f/∂x at a point (a,b)?

The derivative of f with respect to x while holding y constant at b

The derivative of f with respect to y while holding x constant at a

The total derivative of f in the x-direction only

The average rate of change of f over a small region around (a,b)

Recent Partial Derivatives Quizzes

Advanced Partial Derivatives: Higher-Order, Differentiability & Laplace Equation

Partial derivatives are fundamental tools in multivariable calculus, allowing us to explore how functions change with respect to each variable independently. This quiz takes you through a wide range of concepts, including...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
Calculate the partial derivative with respect to y for the function f(x, y) = x³ * tan(y) + 4x.

X³ * sec²(y)

3x² * tan(y) + 4

X³ * sec(y)

3x² * sec²(y)

Partial Derivatives Basics: First-Order Derivatives & Rate-of-Change Interpretation

Partial derivatives allow us to study how a multivariable function changes when one variable varies while the others remain fixed. They play a central role in multivariable calculus, appearing in geometry, optimization, physics,...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
What is the partial derivative of f(x, y) = 3x²y + 4y³ with respect to x?

6xy

6xy + 12y²

3x² + 12y²

3x² + 4y³