Inverse and Inverse Trig Derivatives

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

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

Front

What is the derivative of arcsin(x)?

Back

The derivative of arcsin(x) is: d/dx [arcsin(x)] = 1 / √(1 - x²).

Front

What is the derivative of arccos(x)?

Back

The derivative of arccos(x) is: d/dx [arccos(x)] = -1 / √(1 - x²).

Front

What is the derivative of arctan(x)?

Back

The derivative of arctan(x) is: d/dx [arctan(x)] = 1 / (1 + x²).

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

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

Front

What is the domain of the arcsin function?

Back

The domain of the arcsin function is [-1, 1].

Front

What is the range of the arccos function?

Back

The range of the arccos function is [0, π].

Tags

CCSS.HSF-BF.B.4D

Front

What is the range of the arctan function?

Back

The range of the arctan function is (-π/2, π/2).

Tags

CCSS.HSF-BF.B.4D