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Chapter 2: Q 36. (page 237)

Fill in the blank:

ddx(tanhx)=________.

Short Answer

Expert verified

ddx(tanhx)=sech2x.

Step by step solution

01

Given Information 

The given expression is ddx(tanhx).

02

Simplification 

ddx(tanhx)=ddx(sinhxcoshx)=ddx(sinhx).coshx-sinhxddx(coshx)cosh2x=coshx.coshx-sinhx.sinhxcosh2x=cosh2x-sinh2xcosh2x=1cosh2x=sech2xTherefore,d(tanhx)dx=sech2x.

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Most popular questions from this chapter

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

Use (a) the h→0definition of the derivative and then

(b) the z→cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23–38.

24.f(x)=x3,x=1

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

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

Use (a) the h→0definition of the derivative and then

(b) the z→cdefinition of the derivative to find f'(c)for each function f and value x=c in Exercises 23–38.

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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?

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(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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