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3-8 Derivatives of Inverse Functions

Learning Targets

Concepts / Definitions

Derivatives of Inverse Functions

If $f$ is differentiable at every point of an interval $I$ and $f’(x)$ is never zero on $I$, then $f$ has an inverse, and $f^{-1}$ is differentiable at every point on the interval $f(I)$.
If $f^{-1}(a) = b$, the inverse function slope relationship relates the derivatives by the equation $(f^{-1})’(a) = \frac{1}{f’(b)}$

Proof of Inverse Sine

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