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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

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

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Differentiation Rules

Concept Quizzes

Differentiation Rules Warmup
Power Rule
Product Rule
Quotient Rule
Chain Rule
Inverse Function Rule
Derivatives of Trig Functions
Using Several Differentiation Rules
Problem Solving - Basic
Problem Solving - Intermediate

Challenge Quizzes

Level 2
Level 3

Differentiation - Power Rule

What is the derivative of \(\displaystyle y=5 x^{3}+\frac{1}{x^{6}}\)?

\( 15x^{2}+7x^{-6} \) \( 15x^{2}-7x^{-6} \) \( 15x^{2}-6x^{-7} \) \( 15x^{2}+6x^{-7} \)

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by Brilliant Staff

What is the derivative of \(-17 x^{16}\)?

\( -x^{17} \) \( -272x^{17} \) \( -17x^{17} \) \( -272x^{15} \)

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by Brilliant Staff

If \( f(x) = \displaystyle{\sum_{k=1}^{n} x^k},\) what is \(\displaystyle{ \lim_{n \rightarrow \infty} \frac{f'(1)}{3n^2+4n+5} }?\)

\[ \frac{1}{6} \] \[ \frac{1}{8} \] \[ {8} \] \[ {6} \]

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by Brilliant Staff

What is the derivative of \( y = \frac{4}{x}+\frac{4}{x^2}?\)

\[ \frac{4}{x^2}+\frac{8}{x^3} \] \[ -\frac{4}{x}-\frac{8}{x^2} \] \[ \frac{4}{x}+\frac{8}{x^2} \] \[ -\frac{4}{x^2}-\frac{8}{x^3} \]

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by Brilliant Staff

What is the derivative of \( x^{15} \)?

\( 15x^{15} \) \( 14x^{15} \) \( 14x^{14} \) \( 15x^{14} \)

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by Brilliant Staff

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