Mathematics

Problem

State the relationship between

\frac{dy}{dx}

\frac{dy}{dt}

and

\frac{dx}{dt}

when both

x

and

y

depend on time

t

and

\dfrac{dx}{dt}\neq0

Intuitive explanation

The chain rule is your key here: when both variables depend on a common parameter, you can "chain" their rates together. Think of $\frac{dy}{dx}$ as measuring how $y$ changes per unit change in $x$ , while $\frac{dy}{dt}$ and $\frac{dx}{dt}$ measure how each changes per unit time—so the rate of $y$ with respect to $x$ should be the ratio of their rates with respect to $t$ . This relationship lets you convert between different perspectives on the same motion.

Intuitive explanation

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