Differential calculus of interval elementary functions and decision-making

The article deals with problems, related to calculation of derivatives of interval-specified functions. 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 the problem of calculating derivatives of elementary interval-specified functions. Previously obtained formulas and methods of finding of 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 allowing calculation of interval derivatives are presented. Formulas of the first type express derivatives in the closed interval form, which requires computation using the apparatus of interval mathematics. But formulas of the second type express derivatives in 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 the calculation of the derivative of interval-defined function is reduced to computation of two ordinary certain functions. Using the aforementioned 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 (cosine, sine, tangent, cotangent), interval inverse trigonometric functions. Formulas 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. noninterval) elementary functions is discussed.