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Differentiation Rules

Excel in math and science

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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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