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Chapter 2: Q4 (page 197)

Express the product and quotient rules in Leibniz/ operator notation.

Short Answer

Expert verified

Productrulef'(x)=ddxg(x))*h(x)+ddxh(x))*g(x)f'(x)=g'(x)h(x)+h'(x)g(x)

Quotient Rule

ddxf(x)=ddxg(x)h(x)ddxf(x)=ddxg(x)*h(x)-ddxh(x)*g(x)(h(x))2

Step by step solution

01

Given Information 

Express the product and quotient rules in Leibniz/ operator notation.

02

Step 2:  Derivative 

Lets consider product of functions

f(x) = g(x)*h(x)

Express the product operator notation

ddxf(x)=ddxg(x)*h(x)f'(x)=ddxg(x))*h(x)+ddxh(x))*g(x)f'(x)=g'(x)h(x)+h'(x)g(x)

03

Derivative 

Lets consider quotient of functions

f(x) = g(x)/h(x)

Express the product operator notation

ddxf(x)=ddxg(x)h(x)ddxf(x)=ddxg(x)*h(x)-ddxh(x)*g(x)(h(x))2f'(x)=g'(x)h(x)-h'(x)g(x)h(x)2

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