This final paper deals with the topic of differential calculus and its application in solving optimization problems. Differential calculus is a field of mathematical analysis that deals with derivatives and their application. Through the application of differential calculus, the intervals of monotonicity are determined, that is, the intervals at which the function falls or rises, the local extreme points of the function or the points at which the function reaches the highest or lowest value, and the intervals of convexity and concavity of the function are determined. It is important for any engineer to know differential calculus, since optimization problems that determine the minimum or maximum value that a function can take are common in engineering. The first chapter of this final paper gives a historical overview of the origin of differential calculus and its creators Sir Isaac Newton and Gottfried Wilhelm Leibniz. The second chapter deals with the definition of the derivative, the derivative of elementary functions, higher order derivatives, tangents and normals, the derivative of parametrically and implicitly given functions, and the differential. The next chapter is devoted to the most important theorems of differential calculus, namely Fermat's theorem, Rolle's theorem, Cauchy's theorem, and Lagrange's theorem. In the fourth chapter, the application of differential calculus is emphasized, with a focus on determining the local extrema of the function of a variable. In the fifth chapter, differential calculus is extended to the functions of the two variables used when one quantity depends on the other two independent quantities. It is explained how local extreme values are determined using first and second order partial derivatives. In the last chapter, the application of differential calculus to optimization problems in engineering is presented