Inverse and Inverse Trig Derivatives

Front

What is the derivative of the inverse function y = arcsin(x)?

Back

The derivative is dy/dx = 1/√(1 - x²), for -1 < x < 1.

Front

What is the derivative of the inverse function y = arccos(x)?

Back

The derivative is dy/dx = -1/√(1 - x²), for -1 < x < 1.

Front

What is the derivative of the inverse function y = arctan(x)?

Back

The derivative is dy/dx = 1/(1 + x²), for all x.

Front

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

Back

If y = f(x) is a one-to-one function, then the derivative of its inverse is given by dy/dx = 1/(dx/dy).

Front

What is the derivative of the inverse function y = arccot(x)?

Back

The derivative is dy/dx = -1/(1 + x²), for all x.

Front

What is the derivative of the inverse function y = arcsec(x)?

Back

The derivative is dy/dx = 1/(|x|√(x² - 1)), for |x| > 1.

Front

What is the derivative of the inverse function y = arccsc(x)?

Back

The derivative is dy/dx = -1/(|x|√(x² - 1)), for |x| > 1.

Front

What is the formula for the derivative of the inverse function y = f⁻¹(x)?

Back

The formula is (f⁻¹)'(x) = 1/(f'(f⁻¹(x))).

Front

What is the domain of the function y = arcsin(x)?

Back

The domain is [-1, 1].

Front

What is the range of the function y = arccos(x)?

Back

The range is [0, π].