Summary: We investigate the underlying structure of the \(n\)th derivative of \(e^{s\sqrt{x}}\) with respect to \(x\). For \(n \in \mathbb{Z}^{+}, \frac{d^{n}}{dx^{n}}e^{s\sqrt{x}}\) can be expressed in terms of spherical modified Bessel functions of second kind in the complex plane. The representation holds for \(n \in \mathbb Z^{-}\), where it represents the particular \(n\)-th antiderivative of \(e^{s\sqrt{x}}\) with all \(n\) constants of integration equal to zero. Our results introduce new connections among mathematical applications and provide some Bessel properties.