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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

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=1+x23x2-4x+1

Use the definition of the derivative to find f'for each function fin Exercises 34-59

f(x)=1x2

Differentiate f(x)=3x+x2in three ways. When you have completed all three parts, show that your three answers are the same:

(a) with the chain rule

(b) with the product rule but not the chain rule

(c) without the chain or product rules.

Each graph in Exercises 31鈥�34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=7x2+8x11-18;f(0)=-2
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