### Derivatives #34

Derivative of an inverse:

$\frac{\mathrm{d}}{\mathrm{d}x}\left(f^{-1}(x)\right) = f'\left(f^{-1}(x)\right)^{-1}.$

Conversation

Smith: Hmm.. The derivative of an inverse is the derivative of f-inverse composite f-inverse of x?

Alam: The derivative of an inverse is the inverse of the composite of the derivative with the inverse.

Smith: So ’tis the composite of the derivative f-inverse with the f-inverse?

Alam: ‘Tis one divided by the derivative of f(x) composited with the f-inverse of x.

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