functionsasinh
The hyperbolic sine inverse, often denoted as asinh(x) or sinh⁻¹(x), is the inverse function of the hyperbolic sine function, sinh(x). The hyperbolic sine function is defined as sinh(x) = (eˣ - e⁻ˣ) / 2. Because sinh(x) is a strictly increasing function, its inverse, asinh(x), is well-defined for all real numbers x.
The explicit formula for the hyperbolic sine inverse is given by asinh(x) = ln(x + √(x² + 1)). This
The derivative of asinh(x) is 1 / √(x² + 1). This property makes it useful in calculus, particularly
The function asinh(x) is an odd function, meaning that asinh(-x) = -asinh(x). It is also continuous and