SUMMARY
The article deals with some problems related to calculation of derivatives of interval-specified functions. These problems are relevant in the study of systems with any level of uncertainty (nondeterministic systems). Specifically we will speak about simple systems described byelementary 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 interval-defined functions are used. Basic definitions related to thederivatives of interval functions are given. We present formulas of two types that allow you to calculate interval derivatives. The first typeformulas express derivatives in the closed interval form, which requires computing using the apparatus of interval mathematics. But formulasof the second type can express derivatives in the open interval form, i.e. in the form of two formulas. Formulas above expresses the lower and the upper limits of the interval representing the derivative. Here finding of the derivative of the interval-defined function is reduced tocomputation of two ordinary certain functions. Using above mathematical apparatus we find 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, arccotangent). Formulas of all derivatives are shown in form of an open interval. The difference between derivatives of interval elementary functions and the derivatives of exact functions (not interval) elementary functions is discussed