Suppose is an invertible

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Suppose

y

is an invertible, differentiable function of

x

. In one or two sentences, explain how knowing the derivative of the inverse function at a point allows a measured rate

\frac{dy}{dt}

to be converted into the corresponding rate

\frac{dx}{dt}

at that same point.

Related theory

Derivatives of Inverse Functions
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of inverse trigonometric functions
Continuity and Differentiability

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