In the physical sense, the derivative - is the rate of change of function.

The derivative of a function changes the coordinates - it's speed, the derivative of a function of speed is accelerated.

Thus, knowing the change in body formula coordinate in space, it is possible to find the speed and acceleration in each coordinate space.

instructions

1

Find the increment of the function: Δ-f = f (x0 + Δ-x) - f (x0). Find the function increment related to the increment of the argument: Δ-f / Δ-x = (f (x0 + Δ-x) - f (x0)) / Δ-x. It is assumed that Δ-x approaches zero. This will be the derivative of the function in **point** x0. In practice, first find the total derivative of the formula, and then substitute the specific value of the argument.

2

For example, f (x) = x ^ 3 - 2x ^ 2 + x + 1, it is necessary to find the derivative **point** x = 4.

2 Find the derivative of f (x) = 3x ^ - 2 * 2x + 1. Find the derivative f '(4) = 3 * 4 ^ 2 - 4 * 4 + 1 = 48 - 16 + 1 = 33.