AP Calculus BC Practice Test 2026 – Your Comprehensive All-in-One Guide to Exam Success!

Derivative of the inverse function is the key idea here. If y = f(x) and f is invertible and differentiable, then x = f^{-1}(y). Using the fact that f(f^{-1}(y)) = y and differentiating both sides with respect to y gives f'(f^{-1}(y)) · (f^{-1})'(y) = 1. Solving for the derivative of the inverse, (f^{-1})'(y) = 1 / f'(f^{-1}(y)). This requires f' to be nonzero at the corresponding x.