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Year 12 Maths Extension 1 (2027) Calculus

Derivatives of inverse functions

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Questions
Question 1
182761

For a differentiable, invertible function \(f\), which expression equals \((f^{-1})'(x)\)?

A.
\(\dfrac{1}{f'\!\left(f^{-1}(x)\right)}\)
B.
\(f'\!\left(f^{-1}(x)\right)\)
C.
\(\dfrac{1}{f'(x)}\)
D.
\(f'(x)\)
\(\dfrac{1}{f'\!\left(f^{-1}(x)\right)}\)

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