Implicit Differentiation Quizzes, Questions & Answers

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Top Trending Implicit Differentiation Quizzes

What Did The Circle Say To The Tangent Line?

Choose and remember the correct letter for each problem and answer the question at the end of the quiz.

Questions: 17 | Attempts: 140 | Last updated: Mar 22, 2025

Sample Question 1
Find dy/dx for x⁷+x⁵+x(-³)

(t) 7x⁶+5x⁴-3x(-⁵) )

(s) 7x⁶+5x⁴-3x(-⁴)

(d) x⁷+5x⁴-3x(-²)

Sample Question 2
Find dy/dx for (2x2 +x)/(x-4)

(t) (2x²-16x-4)/(x-4)²

(e) (x²-8x-4)/(x-4)

(h)(2x²-16x-2)/(x-2)

Are you ready to differentiate without solving for y? In this quiz, you’ll learn the basics of implicit differentiation by working with equations where x and y are mixed together. You’ll practice differentiating both...

Questions: 15 | Attempts: 12 | Last updated: Dec 16, 2025

Sample Question 1
What is the first step when finding dy/dx for the equation x² + y² = 25 using implicit differentiation?

Substitute y = 0 into the equation

Solve for y explicitly before differentiating

Differentiate both sides of the equation with respect to x

Move all terms to one side of the equation

Sample Question 2
Find dy/dx for x³ + y³ = 8.

Dy/dx = -x²/y²

Dy/dx = x²/y²

Dy/dx = x² + y²

Dy/dx = -3x²/3y²

Recent Implicit Differentiation Quizzes

Implicit Differentiation Applications & Related Rates

Ready for real-world and advanced applications? This quiz pushes your implicit differentiation skills through complex equations, second derivatives, related rates, and applied scenarios from physics, chemistry, economics, and...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
For x³ + y³ = 3xy, find dy/dx.

(y² - x²)/(y² - x²)

(y - x²)/(y² - x)

(y - x²)/(y² - x)

-(y² - x²)/(x² + y²)

Implicit Differentiation: Second Derivatives & Critical Points

Step into college-level calculus with this quiz on advanced implicit differentiation. You’ll work with challenging relations involving exponentials, logarithms, trigonometric functions, and second derivatives. You’ll...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
Given the equation x² + y² = 25, find dy/dx using implicit differentiation.

-x/y

-y/x

Y/x

X/y

Implicit Differentiation with Exponentials and Logarithms

Ready to dig deeper? In this quiz, you’ll explore the core concepts behind implicit differentiation, focusing on why the chain rule makes everything work. You’ll differentiate equations involving trigonometric and...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
What is the fundamental principle that makes implicit differentiation work?

The power rule can be applied to any equation

The chain rule accounts for the relationship between x and y when y is a function of x

Implicit differentiation only works for circles and ellipses

We can interchange x and y in any equation

Implicit Differentiation with Products & Mixed Terms

Think you’ve got the idea of implicit differentiation? This quiz helps you build confidence with more involved equations, including product terms, powers of y, and expressions that require careful algebra. You’ll...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
What does the chain rule tell us about differentiating terms with y when y is a function of x?

Terms with y have a derivative of 0

Terms with y keep their original coefficient only

We multiply by dy/dx when differentiating terms with y

We ignore terms with y in the differentiation process