Explain, in one or two sentences, why differentiating the formula with respect to…

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

Problem

Explain, in one or two sentences, why differentiating the formula

V = \frac{4}{3}\pi r^{3}

with respect to time

t

gives

\dfrac{dV}{dt} = 4\pi r^{2}\dfrac{dr}{dt}

Related theory

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

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