Differentiating Inverse Functions
Definition
Differentiating inverse functions involves finding the derivative of a function and its inverse. The key idea is that if two functions are inverses of each other, their derivatives are reciprocals of each other.
Analogy
Think of a pair of siblings who have opposite personalities. When you differentiate one sibling's traits (function), you get certain characteristics. But when you differentiate the other sibling's traits (inverse function), you get completely different characteristics that complement and complete each other.
Related terms
Inverse Trigonometric Functions: Inverse trigonometric functions are used to find angles given specific trigonometric ratios. They have corresponding derivatives that can be found using techniques like chain rule.
Logarithmic Differentiation: Logarithmic differentiation is a technique used when differentiating complicated functions involving logarithms. It uses properties of logarithms and differentiation rules to simplify calculations.
Implicit Function Theorem: The implicit function theorem provides conditions under which an equation defines a differentiable function implicitly. It helps in determining whether an equation has an implicit solution or not.
Are you a college student?
Study guides for the entire semester
200k practice questions
Glossary of 50k key terms - memorize important vocab
Resources
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.