In addition to the strict formation of the concepts of derivation and integration it is important to understand their role and purpose outside of the mathematical context. In this paper we give them meaning in the fields of physics and ecnonomics. The mathematical introduction of these concepts is appropriate for students in the fourth grade of high schoold and the first year of technical faculties. In the first chapter we are introduced to the interpretation of derivation, both physical and geometric. We got acquainted with the definition of derivation and the basic rules of derivation. We mentioned methods of deriving implicit and parametrically given functions. With the help of few short examples, we were introduced to derivation in context and finally, using an economic and physical model we presented derivation in „everyday life“. In the second chapter, we are introduced to integrals, both definite and indefinite. We have shown how definite and indefinite integrals are introduced in teaching. Then we introduced the basic theorem of differential and integral calculus, which is the connection between the derivative and the integral, and thus one of the most important theorems in mathematics. After that, with the help of few short examples, we presented integral in the context, and finally, with the help of few examples from the field of economics and physics we presented the use of integrals in „everyday life“.