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Chapter 2: Q 36. (page 237)

Fill in the blank:
$\frac{d}{d x} (\tan h x) =________.$

Short Answer

Expert verified

$\frac{d}{d x} (\tan h x) = s e c h^{2} x .$

Step by step solution

01

Given Information

The given expression is $\frac{d}{d x} (\tan h x) .$

02

Simplification

$\frac{d}{d x} (\tan h x) = \frac{d}{d x} (\frac{\sin h x}{\cos h x}) = \frac{\frac{d}{d x} (\sin h x) . \cos h x - \sin h x \frac{d}{d x} (\cos h x)}{\cos h^{2} x} = \frac{\cos h x . \cos h x - \sin h x . \sin h x}{\cos h^{2} x} = \frac{\cos h^{2} x - \sin h^{2} x}{\cos h^{2} x} = \frac{1}{\cos h^{2} x} = s e c h^{2} x T h e r e f o r e, \frac{d (\tan h x)}{d x} = s e c h^{2} x .$

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