Q:
# What are the derivatives of inverse functions?

The derivative of an inverse function is a calculation of the slope at a particular point of a function that acts in the reverse manner of another function. It is typically denoted as the function f(x) taken to the power of negative one, followed by an apostrophe.

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For example, for the function y = f(x), the inverse is x = f^-1(y). The derivative with respect to x is calculated using the chain rule, where the derivative of the inverse function over dy times dy/dx becomes the derivative of the inverse function over dy times df/dy. When evaluated, the derivative of the inverse function over dy equals one over the derivative of the original function. For example, the derivative of the inverse function of sin(x) is equal to 1/sqrt(1 - x^2).

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