If and are functions of

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

18. If

u, v

and

w

are functions of

x

, then show that

\frac{d}{d x}(u \cdot v \cdot w)=\frac{d u}{d x} v \cdot w+u \cdot \frac{d v}{d x} \cdot w+u \cdot v \frac{d w}{d x}

in two ways - first by repeated application of product rule, second by logarithmic differentiation.

Related theory

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

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