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Differentiation Rules

Concept Quizzes

Rules of Differentiation warmup
Differentiation - Power Rule
Differentiation - Product Rule
Differentiation - Quotient Rule
Chain Rule
Differentiation of Inverse Functions
Applying Differentiation Rules to Trigonometric Functions
Applying Multiple Differentiation Rules
Differentiation Rules Warmup
Differentiation Rules Problem Solving

Challenge Quizzes

Differentiation Rules: Level 2 Challenges
Differentiation Rules: Level 3 Challenges

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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