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- Inverse And Inverse Trig Derivatives
Inverse and Inverse Trig Derivatives
Flashcard
•
Mathematics
•
10th Grade - University
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
Used 1+ times
FREE Resource
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the derivative of the inverse function f^{-1}(x)?
Back
The derivative of the inverse function f^{-1}(x) is given by: (f^{-1})'(x) = 1 / f'(f^{-1}(x)).
Tags
CCSS.HSF-BF.B.4A
2.
FLASHCARD QUESTION
Front
Define the term 'inverse trigonometric functions'.
Back
Inverse trigonometric functions are functions that reverse the action of the standard trigonometric functions. They include arcsin, arccos, and arctan.
Tags
CCSS.HSF.TF.B.7
3.
FLASHCARD QUESTION
Front
What is the derivative of arcsin(x)?
Back
The derivative of arcsin(x) is: d/dx [arcsin(x)] = 1 / √(1 - x²).
4.
FLASHCARD QUESTION
Front
What is the derivative of arccos(x)?
Back
The derivative of arccos(x) is: d/dx [arccos(x)] = -1 / √(1 - x²).
5.
FLASHCARD QUESTION
Front
What is the derivative of arctan(x)?
Back
The derivative of arctan(x) is: d/dx [arctan(x)] = 1 / (1 + x²).
6.
FLASHCARD QUESTION
Front
How do you find the derivative of an inverse function at a specific point?
Back
To find the derivative of an inverse function at a specific point, use the formula: (f^{-1})'(x) = 1 / f'(f^{-1}(x)).
Tags
CCSS.HSF-BF.B.4A
7.
FLASHCARD QUESTION
Front
What is the relationship between a function and its inverse regarding derivatives?
Back
The derivative of a function and its inverse are reciprocals of each other at corresponding points.
Tags
CCSS.HSF-BF.B.4A
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