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Chapter 2: Q. 35 (page 237)

Fill in the blanks to differentiate each of the given basic functions. You may assume that k, m, and b are appropriate constants:
$\frac{d}{d x} (\cos h x)$

Short Answer

Expert verified

The solution is $\frac{d}{d x} (\cos h x) = \sin h x .$

Step by step solution

01

Step 1. Given information

The given function is $\frac{d}{d x} (\cos h x) .$

02

Step 2. Calculation

We have,

$\frac{d}{d x} (\cos h x) \cos h x = \frac{e^{x} + e^{- x}}{2}$

Taking derivative on both sides

$\frac{d}{d x} (\cos h x) = \frac{d}{d x} (\frac{e^{x} + e^{- x}}{2}) = \frac{d}{d x} (\frac{e^{x}}{2}) + \frac{d}{d x} (\frac{e^{- x}}{2}) = \frac{e^{x}}{2} - \frac{e^{- x}}{2} = \frac{e^{x} - e^{- x}}{2} = \sin h x$

Hence, $\frac{d}{d x} (\cos h x) = \sin h x$

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Most popular questions from this chapter

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

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