Question

If a quantity \(y\) varies with another quantity \(x\) based on the rule \(y=f(x)\), which expression represents the rate of change of \(y\) with respect to \(x\)?

Options

• \[\frac{dx}{dt}\]

• \[\frac{dx}{dy}\]

• \[\frac{dy}{dt}\]

• \[\frac{dy}{dx}\]

Answer 1

The derivative \[\frac{dy}{dx}\], or \[f'(x)\], represents the rate of change of \(y\) with respect to \(x\).
It describes how \(y\) changes as \(x\) changes.