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2 ημέρες πριν · The inverse hyperbolic tangent tanh^(-1)z (Zwillinger 1995, p. 481; Beyer 1987, p. 181), sometimes called the area hyperbolic tangent (Harris and Stocker 1998, p. 267), is the multivalued function that is the inverse function of the hyperbolic tangent.
- Inverse Hyperbolic Functions
The inverse hyperbolic functions, sometimes also called the...
- Inverse Hyperbolic Functions
In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent.
The hyperbolic tangent function is also one-to-one and invertible; its inverse, \tanh^{-1} x, is shown in green. It is defined only for -1 x 1 . Just as the hyperbolic functions themselves may be expressed in terms of exponential functions, so their inverses may be expressed in terms of logarithms.
18 Νοε 2019 · If $t=\tanh\frac{x}{2}$, prove that $\sinh x = \frac{2t}{1-t^2}$ and $\cosh x = \frac{1+t^2}{1-t^2}$.
• understand the meaning of the inverse functions sinh−1 x, cosh−1 x and tanh−1 x and spec- ify their domains, • define the reprocal functions sechx, cschx and cothx.
2 ημέρες πριν · The inverse hyperbolic functions, sometimes also called the area hyperbolic functions (Spanier and Oldham 1987, p. 263) are the multivalued function that are the inverse functions of the hyperbolic functions. They are denoted cosh^(-1)z, coth^(-1)z, csch^(-1)z, sech^(-1)z, sinh^(-1)z, and tanh^(-1)z.
29 Αυγ 2023 · You can use either the general formula for the derivative of an inverse function or the above formulas to find the derivatives of the inverse hyperbolic functions: For example, here is one way to find the derivative of \(\tanh^{-1} x\):
