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Calculus

Implicit Differentiation

Excel in math and science

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

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

Excel in math and science

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

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

Excel in math and science

Master concepts by solving fun, challenging problems.

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

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

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, conceptual quizzes.

Our wiki is made for math and science

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

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

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, conceptual quizzes.

Our wiki is made for math and science

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

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

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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
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View solution

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by Brilliant Staff

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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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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

Implicit Differentiation

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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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

Concept Quizzes

Challenge Quizzes

Implicit Differentiation - Inverse Trigonometric Functions

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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

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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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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

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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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

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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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

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, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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

Master advanced concepts through explanations,
examples, and problems from the community.

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

Master advanced concepts through explanations,
examples, and problems from the community.

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

Master advanced concepts through explanations,
examples, and problems from the community.

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

Master advanced concepts through explanations,
examples, and problems from the community.

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

Master advanced concepts through explanations,
examples, and problems from the community.

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

Master advanced concepts through explanations,
examples, and problems from the community.

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

Master advanced concepts through explanations,
examples, and problems from the community.

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