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 the formula: (f^{-1})'(x) = 1 / f'(f^{-1}(x)).

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.

Front

What is the derivative of arcsin(x)?

Back

The derivative of arcsin(x) is 1 / √(1 - x²).

Front

What is the derivative of arccos(x)?

Back

The derivative of arccos(x) is -1 / √(1 - x²).

Front

What is the derivative of arctan(x)?

Back

The derivative of arctan(x) is 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)) and evaluate at the desired x.

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.

Front

What is the derivative of the function y = sin^{-1}(x)?

Back

The derivative of y = sin^{-1}(x) is dy/dx = 1 / √(1 - x²).

Front

What is the derivative of the function y = cos^{-1}(x)?

Back

The derivative of y = cos^{-1}(x) is dy/dx = -1 / √(1 - x²).

Front

What is the derivative of the function y = tan^{-1}(x)?

Back

The derivative of y = tan^{-1}(x) is dy/dx = 1 / (1 + x²).