   Chapter 3.11, Problem 38E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the derivative. Simplify where possible.38. f ( t ) = 1 + sinh t 1 − sinh t

To determine

To find: The derivative of the function.

Explanation

Given:

The function f(t)=1+sinht1sinht.

Derivative rules used:

(1) The chain rule: dydx=dydududx.

(2) The derivative of the hyperbolic cosine function is, ddx(coshx)=sinhx.

Calculation:

The derivative of the function f(t)=1+sinht1sinht is computed as follows,

f(t)=ddt(1+sinht1sinht)

Apply the quotient rule and simplify the terms,

f(t)=(1sinht)ddt(1+sinht)(1+sinht)ddt(1sinht)(1sinht)2=(1sinht)ddt(1+sinht)(1+sinht)ddt(1sinht)(1

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