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)).

Front

Define the term 'inverse trigonometric functions'.

Back

Inverse trigonometric functions are functions that reverse the action of the standard trigonometric functions, allowing us to find angles when given a ratio. Examples 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?

Back

To find the derivative of an inverse function, use the formula (f^{-1})'(x) = 1 / f'(f^{-1}(x)).

Front

What is the relationship between a function and its inverse regarding derivatives?

Back

If f and f^{-1} are inverse functions, then f'(f^{-1}(x)) * (f^{-1})'(x) = 1.

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].

Front

What is the range of the arctan function?

Back

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