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Chapter 2: Q. 89 (page 200)

use the definition of the derivative to prove the quotient rule

Short Answer

Expert verified

We use the definition of derivative to prove the quotient rule

Step by step solution

01

Given information

We are given a function of the formf(x)g(x)

02

use the definition to find the derivative

We get,

limh→0f(x+h)g(x+h)-f(x)g(x)hlimh→0f(x+h)g(x)-g(x+h)f(x)g(x+h)g(x)hlimh→0f(x+h)g(x)-f(x)g(x)+f(x)g(x)-g(x+h)f(x)g(x+h)g(x)hlimh→0g(x)[f(x+h)-f(x)]-f(x)[g(x+h)-g(x)]g(x+h)g(x)hlimh→0g(x)f(x+h)-f(x)h-f(x)g(x+h)-g(x)hg(x+h)g(x)=g(x)f'(x)-f(x)g'(x)[g(x)]2

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