Practice Differentiation Rules in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A set of standard formulas for finding derivatives of common function types without using the limit definition each time.

Shortcuts so you don't have to use the limit definition every time.

Showing a random 20 of 50 problems.

Example 1

medium
Use the quotient rule to differentiate f(x)=x2+1x−3f(x) = \dfrac{x^2 + 1}{x - 3}.

Example 2

easy
Differentiate f(x)=x5f(x) = x^5 using the power rule.

Example 3

medium
Find f′(x)f'(x) when f(x)=x2ln⁡xf(x) = x^2 \ln x.

Example 4

easy
Use the product rule to differentiate f(x)=x3⋅sin⁡xf(x) = x^3 \cdot \sin x.

Example 5

medium
Differentiate f(x)=x2sin⁡xf(x) = x^2 \sin x using the product rule.

Example 6

medium
Differentiate f(x)=e5xf(x) = e^{5x}.

Example 7

medium
Differentiate f(x)=(x2+3)(2x−1)f(x) = (x^2 + 3)(2x - 1) using the product rule.

Example 8

hard
Differentiate f(x)=sin⁡2xf(x) = \sin^2 x.

Example 9

easy
Differentiate f(x)=1xf(x) = \frac{1}{x}.

Example 10

easy
Differentiate f(x)=3x2+2x−7f(x) = 3x^2 + 2x - 7.

Example 11

medium
Differentiate f(x)=ln⁡xxf(x) = \dfrac{\ln x}{x}.

Example 12

challenge
Find the second derivative of f(x)=x4−3x2f(x) = x^4 - 3x^2.

Example 13

easy
Differentiate f(x)=7f(x) = 7.

Example 14

hard
Differentiate f(x)=exx2+1f(x) = \dfrac{e^x}{x^2 + 1} using the quotient rule.

Example 15

hard
Find the slope of y=e2xy = e^{2x} at x=1x = 1.

Example 16

easy
Differentiate f(x)=ln⁡xf(x) = \ln x.

Example 17

easy
Differentiate f(x)=x10f(x) = x^{10}.

Example 18

hard
Differentiate f(x)=xxf(x) = x^x for x>0x > 0.

Example 19

medium
Differentiate f(x)=tan⁡xf(x) = \tan x (express using sec⁡\sec).

Example 20

easy
Differentiate f(x)=6xf(x) = 6x using the constant multiple rule.
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