According to the curriculum, in mathematics the differential calculus is studied in the 9th grade, sciences. The main mathematical concepts introduced are: the increment of argument, the increment of function, the average speed and the instantaneous speed of the function of variation, the derivative of a function at a point, the derivative of a function on a closed interval, chord, tangent, the gradient of a chord and the gradient of the tangent, the equation of the tangent at the given point, derivable functions, lateral derivates, the differential of a function. The definition of the derivative of the function y=f(x) at a given point is introduced by lim of the ratio of the increment of the function to the increment of the argument, while the increment of the argument approaches 0. f x        )()( lim)( 00 0 0 The concepts of lateral derivatives are introduced in the same way: If there takes place the equality       000 xfxfxf ds     then it is said that the function f is derivable at the point x=x. The differential of a function is defined as a function of a variable dx, if we have the differentiable function f:D→R, y =f(x), then the function df(x)=f'(x0)dx, where f(x0) is the derivative of the function at the point x0, dx is the differential of the argument, is called the differential of a function f in x = x0. The applicability of the differential in the approximate calculus: 1. the monotony of function; 2. the extremes of a function; 3. the maximum and minimum values of a function at the given interval; 4. tracing the graphs of functions; 5. solving problems of extremes; 6. modeling technical and economical problems.