Brilliant

Home Courses Today

Excel in math and science.

Log in with Facebook Log in with Google Log in with email

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

Sign up to access problem solutions.

That seems reasonable. Find out if you're right!

Sign up to save your progress!

Log in with Facebook Log in with Google Log in with email

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

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}-6x^{-7}

15x^{2}+6x^{-7}

15x^{2}-7x^{-6}

Show explanation

View wiki

by Brilliant Staff

What is the derivative of $-17 x^{16}$ ?

-272x^{15}

-17x^{17}

-272x^{17}

-x^{17}

Show explanation

View wiki

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}

{6}

{8}

Show explanation

View wiki

by Brilliant Staff

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

\frac{4}{x}+\frac{8}{x^2}

\frac{4}{x^2}+\frac{8}{x^3}

-\frac{4}{x^2}-\frac{8}{x^3}

-\frac{4}{x}-\frac{8}{x^2}

Show explanation

View wiki

by Brilliant Staff

What is the derivative of $x^{15}$ ?

15x^{15}

14x^{14}

14x^{15}

15x^{14}

Show explanation

View wiki

by Brilliant Staff

×

Problem Loading...

Note Loading...

Set Loading...