The derivative of the inverse hyperbolic function is the reciprocal of the derivative of the corresponding hyperbolic function. For example, the derivative of the inverse hyperbolic cosine function (arccosh) is 1/sqrt(x^2 - 1).
The general formula for finding the derivative of inverse hyperbolic functions is: d/dx(arccosh(x)) = 1/sqrt(x^2 - 1), d/dx(arcsinh(x)) = 1/sqrt(x^2 + 1), and d/dx(arctanh(x)) = 1/(1 - x^2).
The chain rule can be used to find the derivative of inverse hyperbolic functions by first rewriting the function in terms of the corresponding hyperbolic function and then using the chain rule on the hyperbolic function.
The derivative of inverse hyperbolic functions are related to the derivative of their corresponding hyperbolic functions through the chain rule. The derivative of the inverse hyperbolic function is the reciprocal of the derivative of the corresponding hyperbolic function.
Yes, there are some special cases when finding the derivative of inverse hyperbolic functions. For example, the derivative of the inverse hyperbolic tangent function (arctanh) is 1/(1 - x^2), but when x = 1 or -1, the derivative is undefined. Similarly, for the inverse hyperbolic secant function (arcsech), the derivative is undefined when x = 0 or 1.