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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

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including olympiad champions, researchers, and professionals.

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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 \(\frac{dy}{dx} ?\)

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

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by Brilliant Staff

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

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

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by Brilliant Staff

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

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

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by Brilliant Staff

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

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

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by Brilliant Staff

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

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

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by Brilliant Staff

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