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Implicit Differentiation

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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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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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