Chapter 2: Q. 93 (page 236)

Prove each of the differentiation formulas in Exercises 93–96. (These exercises involve hyperbolic functions.)
$\frac{d}{d x} (\cos h x) = \sin h x$

Short Answer

Expert verified

We proved the formula $\frac{d}{d x} (\cos h x) = \sin h x$ .

Step by step solution

Step 1. Given Information

We need to prove the hyperbolic function $\frac{d}{d x} (\cos h x) = \sin h x$ .

Step 2. Proving the function

$\frac{d}{d x} (\cos h x) = \frac{d}{d x} (\frac{e^{x} + e^{- x}}{2}) = \frac{1}{2} \frac{d}{d x} (e^{x}) + \frac{d}{d x} (e^{- x}) = \frac{1}{2} (e^{x} - e^{- x}) = \sin h x$

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Prove each of the differentiation formulas in Exercises 93–96. (These exercises involve hyperbolic functions.)
$\frac{d}{d x} (\cos h x) = \sin h x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the function

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Prove each of the differentiation formulas in Exercises 93–96. (These exercises involve hyperbolic functions.)ddxcoshx=sinhx

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the function

One App. One Place for Learning.

Most popular questions from this chapter

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Prove each of the differentiation formulas in Exercises 93–96. (These exercises involve hyperbolic functions.)
$\frac{d}{d x} (\cos h x) = \sin h x$