How do you apply implicit differentiation to the equation $$2x^2 - 3y^2 = 4$$ ?

Differentiate both sides with respect to x, treating y as a function of x. This gives $$\frac{d}{dx}(2x^2) - \frac{d}{dx}(3y^2) = 0$$ , leading to $$\frac{dy}{dx} = \frac{2x}{3y}$$ .

What is the derivative of $$y^2 = 10x$$ using implicit differentiation?

Differentiate both sides: $$2y \frac{dy}{dx} = 10$$ , leading to $$\frac{dy}{dx} = \frac{5}{y}$$ .

How do you find $$\frac{dy}{dx}$$ for the equation $$xy + y^2 = 2$$ ?

Differentiate both sides: $$x \frac{dy}{dx} + y + 2y \frac{dy}{dx} = 0$$ , leading to $$\frac{dy}{dx} = -\frac{y}{x + 2y}$$ .

What is the derivative of $$x^2 + xy + y^3 = 0$$ ?

Using implicit differentiation, differentiate to get $$2x + y + x \frac{dy}{dx} + 3y^2 \frac{dy}{dx} = 0$$ , leading to $$\frac{dy}{dx} = -\frac{2x + y}{x + 3y^2}$$ .

What is the significance of the implicit function theorem?

The implicit function theorem provides conditions under which a relation defines a function implicitly, allowing for the differentiation of y with respect to x.

How do you find the slope of a tangent line using implicit differentiation?

To find the slope of the tangent line at a point, compute $$\frac{dy}{dx}$$ at that point using implicit differentiation.

What is the relationship between implicit differentiation and related rates?

Implicit differentiation is often used in related rates problems to find the rate of change of one variable with respect to another when both are related by an equation.

What is the first step in solving an implicit differentiation problem?

The first step is to differentiate both sides of the equation with respect to x, applying the chain rule for terms involving y.

How do you handle higher-order derivatives in implicit differentiation?

Higher-order derivatives can be found by repeatedly applying implicit differentiation and using the results of previous derivatives.

What is the role of the variable y in implicit differentiation?

In implicit differentiation, y is treated as a function of x, allowing us to differentiate terms involving y with respect to x.

What is an example of an implicit function?

An example of an implicit function is $$x^2 + y^2 = 1$$ , which represents a circle.

Why is implicit differentiation useful?

Implicit differentiation is useful because it allows us to find derivatives of functions that are not easily solvable for y, especially in complex equations.

Implicit differentiation Review Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y, rather than explicitly solving for y.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the chain rule in the context of implicit differentiation?

Back

The chain rule states that if y is a function of x, then the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

7.

FLASHCARD QUESTION

Front

What is the product rule in differentiation?

Back

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

10 questions

Ukrainian Language Learning

Flashcard

•

University

10 questions

Narrative Text

Flashcard

•

11th Grade

7 questions

How to Make a Cup of Tea

Flashcard

•

12th Grade

10 questions

Cuestionario sobre CV y Resumen

Flashcard

•

12th Grade

9 questions

The Forgetting Curve

Flashcard

•

12th Grade

10 questions

Review - Proving Congruent Triangles

Flashcard

•

KG - University

10 questions

Unit 104 SITE PREP

Flashcard

•

Professional Development

10 questions

Can you...?

Flashcard

•

Professional Development

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

20 questions

Figurative Language Review

Quiz

•

6th Grade

Discover more resources for Mathematics

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

13 questions

Model Exponential Growth and Decay Scenarios

Quiz

•

9th - 12th Grade

27 questions

7.2.3 Quadrilateral Properties

Quiz

•

9th - 12th Grade

10 questions

Key Features of Quadratic Functions

Interactive video

•

8th - 12th Grade

11 questions

Exponent Quotient Rules A1 U7

Quiz

•

9th - 12th Grade

18 questions

Integer Operations

Quiz

•

5th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems

Quiz

•

9th - 12th Grade

10 questions

complementary and Supplementary angles

Quiz

•

9th - 12th Grade