Question

If y = f(x) and (x) depends on time (t), then \[\frac {df}{dt}\]​ equals ______.

Options

• \[\frac{df}{dx}+\frac{dx}{dt}\]

• \[\frac{df}{dx}\times\frac{dx}{dt}\]

• \[\frac{dx}{dt}\div\frac{df}{dx}\]

• \[\frac{df}{dx}-\frac{dx}{dt}\]

Answer 1

If y = f(x) and (x) depends on time (t), then \[\frac {df}{dt}\]​ equals \[\frac{df}{dx}\times\frac{dx}{dt}\].

Explanation:

This is the chain rule of differentiation. When a function depends on an intermediate variable, the rate of change with respect to time is the product of the two individual rates of change.