Math Practice

Derivatives of Exponential and Logarithmic Functions Practice Problems

Use the rules for eˣ, aˣ, ln x and log x, plus the product, quotient and chain rules where a problem needs them. The exponential keeps its form; the log becomes the derivative of the inside over the inside.

Questions

1.
Differentiate . Type as e^x.
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is its own derivative, so .
2.
Differentiate . Put the exponent in brackets: e^(4x).
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Chain rule: .
3.
Differentiate . Type the natural log as ln( ).
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, so . It is not : the variable is in the exponent, so the power rule doesn't apply.
4.
Differentiate .
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Chain rule: . Or use the log rules first: , and is a constant.
5.
Differentiate .
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The exponent is , with derivative : .
6.
Differentiate .
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Product rule: .
7.
Differentiate .
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Derivative of the inside over the inside: .
8.
Differentiate . Type the natural log with brackets, as ln(x).
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Product rule: .
9.
Differentiate . Use ln( ) in your answer.
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, so .
10.
Differentiate .
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Quotient rule: .
11.
Differentiate .
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Derivative of the inside over the inside: .
12.
Find the slope of the tangent line to at .
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. At : .

Written by

Zohaib

MPhil in Mathematics, Founder of Mathovia

Published

14 October 2026

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Derivatives of Exponential and Logarithmic Functions Practice Problems

These problems follow the derivatives of exponential and logarithmic functions lesson. They start with the four basic rules and build up to the chain, product and quotient rules.

The four rules

and
and
With an inside function : and

Common mistakes to watch for

Using the power rule on an exponential: does not become .
Forgetting the derivative of the exponent in or .
Writing for the derivative of ; the 5s cancel to .
Leaving out in the derivatives of and .

Frequently Asked Questions

How do I type e^x and ln?+

Type e^x for e to the x, and put a longer exponent in brackets, such as e^(4x) or e^(x^2). Type the natural log as ln( ), for example ln(x) + 1 or 7^x*ln(7).

Do I need to simplify my answer?+

No. Any expression equal to the correct derivative is accepted, so e^x*(1 + x) and e^x + x*e^x are both marked correct.

(ln x)′Derivatives of Exponential and Logarithmic Functions Practice Problems

Derivatives of Exponential and Logarithmic Functions Practice Problems

The four rules

Common mistakes to watch for

Frequently Asked Questions

More practice problems

Derivatives of Exponential and Logarithmic Functions Practice Problems