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Chapter 2: Q 25 (page 238)

: Find the derivatives of the function

f(x)=tanh3x5

Short Answer

Expert verified

dydx=12tanh3x5.3tanh2x5.sech2x5.5x4

Step by step solution

01

Step 1:Given information

The given expression isf(x)=tanh3x5

02

Step 2:Simplification

Given

f(x)=y=tanh3x5

Differentiating w.r.t x

=12tanh3x5.3tanh2x5.ddxtanhx5

=12tanh3x5.3tanh2x5.sech2x5.ddxx5

=1tanh3x5.3tanh2x5.sech2x5.5x4

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Most popular questions from this chapter

Use the definition of the derivative to find f'for each function fin Exercises39-54

f(x)=21-x

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)=(x4-8)(1-3x5);f(0)=2

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

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

25.f(x)=1x,x=-1

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 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)=xx+1-2
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