Question

When \(x\) and \(y\) both vary with respect to \(t\), which formula gives the rate of change of \(y\) with respect to \(x\)?

Options

• \[\frac{dy}{dx}=\frac{dy}{dt}+\frac{dx}{dt}\]

• \[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\]

• \[\frac{dy}{dx}=\frac{\frac{dx}{dt}}{\frac{dy}{dt}}\]

• \[\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dx}{dt}\]

Answer 1

The Chain Rule for Rates is \[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\].
It converts rates with respect to the third variable \(t\) into a rate of \(y\) with respect to \(x\).