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

f(x)=x2-1x2-x-2

Short Answer

Expert verified

The derivative isf'(x)=2xx2-x-2-(2x-1)x2-1x2-x-22

Step by step solution

01

Given information

Given functionf(x)=x2-1x2-x-2

02

Use the chain rule and calculate

Calculating, we get

f(x)=x2-1x2-x-2f'(x)=(x2-x-2)(2x)-(x2-1)(2x-1)(x2-x-2)2f'(x)=2x(x2-x-2)-(2x-1)(x2-1)(x2-x-2)2

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Most popular questions from this chapter

Stuart left his house at noon and walked north on Pine Street for 20minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart’s house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist’s office. When he got there, he found the office closed for lunch; he was 10minutes early for his 12:40appointment. Stuart waited at the office for 10minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart’s position over time. Then sketch a graph that describes Stuart’s velocity over time.

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 the equations of the lines described in Exercises 59-64.

The line tangent to the graph of y=4x+3 at the point(-2,-5)

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

f(x)=x(3x2+1)9

For each function f that follows find all the x-values in the domain of f for which f'(x)=0and all the values for which f'(x)does not exist in later section we will call these values the critical points of f

localid="1648604345877" a)f(x)=x3-2xb)f(x)=x-xc)f(x)=11+xd)f(x)=x2(x-1)(x-2)2

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