Chapter 2: Q. 34 (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:
$\frac{d}{d x} (\sin h x) =____$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

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

Step 2. Calculation

We have,

$\frac{d}{d x} (\sin h x)$

$\sin h x = \frac{e^{x} - e^{- x}}{2}$

Taking derivative on both sides.

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

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

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Fill in the blanks to differentiate each of the given basic functions. You may assume that k, m, and b are appropriate constants:ddx(sinhx)=____

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Decision Maths

Study anywhere. Anytime. Across all devices.

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