In the physical sense, the derivative is the rate of change of the function.
The derivative of the coordinate change function is the speed of motion, the derivative of the velocity function is the acceleration.
Thus, knowing the formula for changing the coordinates of a body in space, you can find its speed and acceleration in each coordinate space.
Find the increment of the function: Δ-f = f (x0 + Δ-x) - f (x0). Find the ratio of the increment of the function to the increment of the argument: Δ-f / Δ-x = (f (x0 + Δ-x) -f (x0)) / Δ-x. In this case, consider that Δ-x tends to zero. This is the derivative of the function in Point X0. In practice, first find the general formula of the derivative of the function, and then substitute a specific value of the argument.
For the example, f (x) = x ^ 3 - 2x ^ 2 + x + 1, we must find the derivative in Point X = 4.
Find the derivative f (x) = 3x ^ 2 - 2 * 2x + 1. Find the derivative f '(4) = 3 * 4 ^ 2 - 4 * 4 + 1 = 48 - 16 + 1 = 33.