Derivatives of interval elementary functions

The problems related to calculation of derivatives of interval-specified functions are considered. These problems are relevant in study of systems with any level of uncertainty (nondeterministic systems). Specifically we speak about simple systems described by elementary interval-specific functions. Accordingly we solved problem of calculating derivatives of elementary interval-specified functions. Previously obtained formulas and methods of finding derivatives of any intervally defined functions are used. Basic definitions related to derivatives of the interval-specified functions are given and formulas of two types that allow you to calculate interval derivatives are presented. The first type formulae express derivatives in the closed interval form, which requires to compute using the apparatus of interval mathematics. But formulae of the second type can express derivatives in the open interval form, i. e. in form of two formulas. Formulas above expresses the lower and the upper limits of the interval representing the derivative. Here finding the derivative of interval-defined function is reduced to computation of two ordinary certain functions. Using above mathematical apparatus we find the derivatives of all elementary interval functions: interval constant, interval power function, interval exponential function, interval logarithmic function, interval natural-logarithmic function, interval trigonometric functions (sine, cosine, tangent, cotangent), interval inverse trigonometric functions (arcsine, arccosine, arctangent and arccotangent). Formulae of all the derivatives are shown in form of an open interval. The difference between derivatives of interval elementary functions and the derivatives of normal (i.e. non-interval) elementary functions is discussed.

interval, interval function, interval derivative, interval computations, interval-differential calculus