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Express the constant multiple, sum, and difference rules in Leibniz/operator notation

Short Answer

Expert verified

ddxf(x)=ddxkddxf(x)=ddxg(x)+ddxh(x)ddxf(x)=ddxg(x)-ddxh(x)

Step by step solution

01

Given Information 

Express the constant multiple, sum, and difference rules in Leibniz/operator notation

02

Constant

Consider a constant function

f(x)=kweneedtoexpressthedifferentiationinoperatornotationddxf(x)=ddxkf'(x)=0

03

Sum

Consider a sum function

f(x)=g(x)+h(x)

express the differentiation in operator notation

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

04

Difference

Consider difference of functions

f(x)=g(x)-h(x)

Express it in operator notation

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

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