Calculus › Section F · Logarithmic, exponential, and other transcendental functions › Topic F.3

Inverse functions and their derivatives

Many famous functions exist only as answers to a reversal question: the square root, the logarithm, the arcsine. Inverse functions have their own theory, and a remarkably clean derivative rule.

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In this topic

Reversing the machine
The definition and one-to-one
Tests: the horizontal line and monotonicity
Worked example: finding and verifying an inverse
Worked example: roots as inverses
The picture: reflection in y = x
The derivative of an inverse
Worked example: the rule, without a formula
Worked example: the cube root, two independent ways
Common mistakes to avoid
Key takeaways

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Standards: 3

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