The function derivative - a child of differential calculus of Newton and Leibniz - has quite certain physical sense if to consider it more deeply.
General meaning of a derivative
The derivative of function is a limit to which the relation of increment of value of function to increment of an argument at aspiration of the last tends to zero. For the unprepared person sounds extremely abstractly. If to understand, it will be visible that it not so.
To find a function derivative, take any function – dependence of "Y" on "X". Replace in expression of this function her argument with increment of an argument and divide the received expression into increment. You receive fraction. Further it is necessary to perform operation of a limit. For this purpose it is necessary to direct increment of an argument to zero and to observe what your fraction will direct to in this case. That final, as a rule, size will also be derivative function. Pay attention that in expression for derivative function there will be any more no increments because you directed to their zero therefore there will be a variable and (or) a constant.
So, the derivative is the relation of increment of function to increment of an argument. What meaning of such size? If you, for example, find a derivative of linear function, then you will see that she is constant. And this constant in expression of the function is just multiplied by an argument. Further, if you construct the schedule of the given function at different values of a derivative, just changing it over and over again, then you will notice that at its great values the inclination of a straight line becomes more and vice versa. If you deal not with linear function, then the value of a derivative in this point will tell you about an inclination of the tangent which is carried out in this point of function. Thus, the value of derivative function speaks about function growth rate in this point.
Physical meaning of a derivative
Now, to understand the physical meaning of a derivative, it is rather simple to replace your abstract function with any physically reasonable. For example, let you have dependence of a way of movement of a body on time. Then derivative of such function will tell you about the speed of movement of a body. If you receive value constant, then it will be possible to say that the body moves evenly, that is with a constant speed. If you receive expression for a derivative, linearly time-dependent, then it will become clear that the movement uniformly accelerated because the second derivative, that is the derivative of this derivative, will be a constant that actually means constancy of speed of speed of a body, and it and is its acceleration. You can pick up any other physical function and see that its derivative will give you a certain physical sense.