Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Section Derivatives of Trigonometric and Hyperbolic Functions states the derivative of Trigonometric Functions, Inverse Trigonometric Functions, Hyperbolic Functions, and Inverse Hyperbolic Functions.

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Step 1. Given information.

The given section topic is Derivatives of Trigonometric and Hyperbolic Functions.

Step 2. Derivatives of the Trigonometric Functions

Derivatives of the Trigonometric Functions are follows

$\frac{d}{d x} (\sin x) = \cos x \frac{d}{d x} (\cos x) = - \sin x \frac{d}{d x} (\tan x) = s e c^{2} x \frac{d}{d x} (s e c x) = s e c x \tan x \frac{d}{d x} (c s c x) = - c s c x c o t x \frac{d}{d x} (c o t x) = - c s c^{2} x$

Step 3. Derivatives of Inverse Trigonometric Functions

Derivatives of Inverse Trigonometric Functions are following.

$\frac{d}{d x} \sin^{- 1} x = \frac{1}{\sqrt{1 - x^{2}}} \frac{d}{d x} \tan^{- 1} x = \frac{1}{1 + x^{2}} \frac{d}{d x} s e c^{- 1} x = \frac{1}{|x| \sqrt{x^{2} - 1}}$

Step 4. Derivatives of Hyperbolic Functions and Inverse Hyperbolic Functions.

Derivatives of Hyperbolic Functions are following.

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

Derivatives of Inverse Hyperbolic Functions are following.
$\frac{d}{d x} \sin h^{- 1} x = \frac{1}{\sqrt{x^{2} + 1}} \frac{d}{d x} \cos h^{- 1} x = \frac{1}{\sqrt{x^{2} - 1}} \frac{d}{d x} \tan h^{- 1} x = \frac{1}{1 - x^{2}}$

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Step 1. Given information.

Step 2. Derivatives of the Trigonometric Functions

Step 3. Derivatives of Inverse Trigonometric Functions

Step 4. Derivatives of Hyperbolic Functions and Inverse Hyperbolic Functions.

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Step 1. Given information.

Step 2. Derivatives of the Trigonometric Functions

Step 3. Derivatives of Inverse Trigonometric Functions

Step 4. Derivatives of Hyperbolic Functions and Inverse Hyperbolic Functions.

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