coth (-x) = -coth x. \displaystyle \text {sinh} (x \pm y) = \text {sinh}\ x \ \text {cosh}\ y \pm \text {cosh}\ x\ \text {sinh}\ y sinh(x±y) = sinh x cosh y ±cosh x sinh y. \displaystyle \text {cosh} (x \pm y) = \text {cosh}\ x\ \text {cosh}\ y \pm \text {sinh}\ x\ \text …

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

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When a variable is denoted by x, the hyperbolic cotangent function is written as coth (x) in mathematics. The derivative of the hyperbolic function with respect to x is written in the following mathematical form in differential calculus. d d x coth x.

We have six main hyperbolic functions given by, sinhx, coshx, tanhx, sechx, cothx, and cschx. The derivative of hyperbolic functions is calculated using the derivatives of exponential functions formula and other hyperbolic functions formulas and identities.

Hyperbolic cosine has a global minimum at x = 0 whose value is y = 1 and it's decreasing from 1 to 0 and increasing from 0 to +1, for this reason we can invert it on the positive half-axis or the negative one. By convention we choose the positive one [0; 1).

Illustrated definition of Coth: The Hyperbolic Cotangent Function. coth (x) (esupxsup esupminusxsup) (esupxsup minus...

It is defined as the ratio of the hyperbolic cosine to the hyperbolic sine of a given angle x. Mathematically, coth (x) can be expressed as: coth (x) = cosh (x) / sinh (x) Here, cosh (x) represents the hyperbolic cosine function and sinh (x) represents the hyperbolic sine function.

Hyperbolic Definitions sinh(x) = ( e x - e-x)/2 . csch(x) = 1/sinh(x) = 2/( e x - e-x) . cosh(x) = ( e x + e-x)/2 . sech(x) = 1/cosh(x) = 2/( e x + e-x) . tanh(x ...

Oct 27, 2018 · 次回は cosec x（=1/sin x）の微分と積分の公式 を解説します。