Brilliant

Practice

Algebra
Geometry
Number Theory
Calculus
Discrete Mathematics
Basic Mathematics
Logic
Classical Mechanics
Electricity and Magnetism
Computer Science
Quantitative Finance
Chemistry

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Log in with Facebook Log in with Google

or

Log in with email

Join using Facebook Join using Google

or

Join using email

New user? Sign up

Existing user? Log in

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

Sign up to access problem solutions.

That seems reasonable. Find out if you're right!

Log in with Facebook Log in with Google

or

Log in with email

Join using Facebook Join using Google

or

Join using email

New user? Sign up

Existing user? Log in

Implicit Differentiation

Concept Quizzes

Polynomials
Rational Functions
Radical Functions
Exponential/Logarithmic Functions
Trigonometric Functions
Inverse Trigonometric Functions
Problem Solving - Basic
Related Rates

Challenge Quizzes

Level 2
Level 3

Implicit Differentiation - Inverse Trigonometric Functions

If \(\displaystyle \tan^{-1} \left(x^2y\right)=3x+6y,\) what is \(\frac{dy}{dx} ?\)

\[\displaystyle{y'=\frac{3+6x^4y^2-2xy}{x^2-3-6x^4y^2}} \] \[\displaystyle{y'=\frac{6+3x^4y^2-2xy}{x^2-6-3x^4y^2}} \] \[\displaystyle{y'=\frac{3+3x^4y^2-2xy}{x^2-6-6x^4y^2}} \] \[\displaystyle{y'=\frac{6+6x^4y^2-2xy}{x^2-3-3x^4y^2}} \]

Show explanation

View wiki

by Brilliant Staff

Given the function \(\tan^{-1}(4xy)=5,\) What is \(\frac{dy}{dx}?\)

\[\displaystyle{ -\frac{y}{x}} \] \[\displaystyle{ \frac{x}{y}} \] \[\displaystyle{ -\frac{x}{y}} \] \[\displaystyle{ \frac{y}{x}} \]

Show explanation

View wiki

by Brilliant Staff

If \(\displaystyle \cos^{-1} \left(\frac{6x-y}{3x+y}\right)=e^a,\) what is \( \frac{dy}{dx} ?\)

\[\displaystyle{ \frac{dy}{dx}=\frac{y}{x}} \] \[\displaystyle{ \frac{dy}{dx}=\frac{x^2}{y^2}} \] \[\displaystyle{ \frac{dy}{dx}=\frac{x}{y}} \] \[\displaystyle{ \frac{dy}{dx}=\frac{y^2}{x^2}} \]

Show explanation

View wiki

by Brilliant Staff

If \(\displaystyle \sin^{-1} (7x^2-y^2)=\ln 6,\) what is \( \frac{dy}{dx} ?\)

\[ \frac{dy}{dx}=\frac{7x}{y} \] \[ \frac{dy}{dx}=\frac{7y}{x} \] \[ \frac{dy}{dx}=\frac{7y^2}{x^2} \] \[ \frac{dy}{dx}=\frac{7x^2}{y^2} \]

Show explanation

View wiki

by Brilliant Staff

Given the function \(\cos^{-1}(3x+11y)=12,\) what is \( \frac{dy}{dx} ?\)

\[ \frac{dy}{dx}=\frac{11}{3} \] \[ \frac{dy}{dx}=\frac{11}{12} \] \[ \frac{dy}{dx}=-\frac{12}{11} \] \[ \frac{dy}{dx}=-\frac{3}{11} \]

Show explanation

View wiki

by Brilliant Staff

×

Problem Loading...

Note Loading...

Set Loading...