Mathematical formulas

Calculus II

Subjects Home Search Guide

Sections

1Notation, domains and conventions
2Indefinite integral and properties
3Definite integral and Fundamental Theorem of Calculus
4Substitution method
5Integration by parts
6Trigonometric integrals
7Trigonometric substitution and quadratic radicals
8Rational functions and partial fractions
9Improper integrals
10Applications of the integral
11Numerical integration
12Parametric curves
13Polar coordinates
14Sequences and series
15Power series and Taylor series
16Elementary differential equations
17Guide to choosing a method
AAppendix A: extensive table of antiderivatives
BAppendix B: useful equivalences

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Formula · Mathematical formulas

Formula

6.8. Hyperbolic functions

Formula

In 6.8. Hyperbolic functions

Formula

\frac{d}{d x} senh x = cosh x, \frac{d}{d x} cosh x = senh x

Variables

$x$ Variable independiente (variable de integración)
$d x$ Diferencial respecto de $x$

Conditions

$\frac{d}{d x} cosh x = senh x$

Related formulas

Related

Formula

cosh^{2} x - senh^{2} x = 1

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Related

Formula

\frac{d}{d x} tanh x = sech^{2} x, \frac{d}{d x} coth x = - csch^{2} x

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Related

Formula

senh x = \frac{e ^{x} - e ^{- x}}{2}, cosh x = \frac{e ^{x} + e ^{- x}}{2}

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Related

Formula

\int tanh x d x = ln (cosh x) + C, \int coth x d x = ln ∣ senh x ∣ + C

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Hyperbolic functions