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Chapter 2: Q3 (page 197)

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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Most popular questions from this chapter

Velocity v(t) is the derivative of position s(t). It is also true that acceleration a(t) (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function s(t), what are the units of s(1.2)? What are the units and real-world interpretation of v(1.2)? What are the units and real-world interpretations of a(1.2)?

Use the definition of the derivative to find ffor each function fin Exercises 39-54

f(x)=1x2-1

The following reciprocal rules tells us hoe to differentiate the reciprocal of a function

ddx(1f(x))=-1[f(x)]2

Prove this using

a) definition of the derivative

b) by using the quotient rule

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The tangent line to f(x)=x2 atx=0

State the chain rule for differentiating a composition g(h(x))of two functions expressed

(a) in “prime” notation and

(b) in Leibniz notation.
See all solutions

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