7. Write a formula for the triple product rule, the derivative of p(x) = f(x) · g(x).h(x)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**7. Write a formula for the triple product rule, the derivative of \( p(x) = f(x) \cdot g(x) \cdot h(x) \)**

This problem asks you to find the derivative of a product of three functions, requiring the use of the triple product rule. The derivative of \( p(x) \) can be determined by extending the product rule. Here's the expression you need:

\[
p'(x) = f'(x) \cdot g(x) \cdot h(x) + f(x) \cdot g'(x) \cdot h(x) + f(x) \cdot g(x) \cdot h'(x)
\]

This rule follows from taking the derivative of each function while multiplying by the other two unaltered functions and then summing the results.
Transcribed Image Text:**7. Write a formula for the triple product rule, the derivative of \( p(x) = f(x) \cdot g(x) \cdot h(x) \)** This problem asks you to find the derivative of a product of three functions, requiring the use of the triple product rule. The derivative of \( p(x) \) can be determined by extending the product rule. Here's the expression you need: \[ p'(x) = f'(x) \cdot g(x) \cdot h(x) + f(x) \cdot g'(x) \cdot h(x) + f(x) \cdot g(x) \cdot h'(x) \] This rule follows from taking the derivative of each function while multiplying by the other two unaltered functions and then summing the results.
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