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Chapter 2: Q. 44 (page 210)

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)=xx2xx23

Short Answer

Expert verified

The required answer is256x196

Step by step solution

01

Step 1. Given Information   

The given function isf(x)=xx2xx23

02

Step 2. Calculation    

Differentiate both the sides with respect to x, we get,

f'(x)=ddxx1+2+12+23=ddxx6+12+3+46=ddxx256=256x256-1=256x196

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Most popular questions from this chapter

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

role="math" localid="1648284617718" f(x)=2x+1

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)鈥�f(x)=11+xd)f(x)=x2(x-1)(x-2)2

Use the definition of the derivative to find f' for each function f in Exercises 39-54

f(x)=-x3-x+1

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)=3x2+18-7x-23

Suppose h(t) represents the average height, in feet, of a person who is t years old.

(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?

(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?

(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?
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