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How to find the derivative at a point

How to find the derivative at a point

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.

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