In the formula used in related-rates problems

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

Problem

In the formula

\dfrac{dy}{dt}=\dfrac{dy}{dx}\,\dfrac{dx}{dt}

used in related-rates problems, briefly explain what each factor represents and why their product gives

\dfrac{dy}{dt}

Related theory

Advanced Differentiation
Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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