Coth

The hyperbolic cotangent is defined by $$\mathrm{coth}(z)=\dfrac{1}{\tanh(z)}=\dfrac{\mathrm{cosh}(z)}{\mathrm{sinh}(z)},$$ where $\tanh$ denotes the hyperbolic tangent function.

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  Plot of $\mathrm{coth}$ on $[-5,5]$.

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  Domain coloring of $\mathrm{coth}$.

Properties

Derivative of coth
Antiderivative of coth
Relationship between coth and csch
Relationship between coth and cot
Relationship between cot and coth
Relationship between csc, Gudermannian, and coth
Relationship between coth, inverse Gudermannian, and csc

Videos

Calculus I - Derivative of Hyperbolic Cotangent Function coth(x) - Proof

See Also

Arccoth

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.5.6

<center>Hyperbolic trigonometric functions

Sinh

Cosh

Tanh

Csch

Sech

Coth

</center>