How to find the derivative at the point

Physical meaning of derivative - rate of change of a function. The derivative of the function changes the coordinates is the rate of motion, the derivative of speed is acceleration. Thus, knowing the formula for change of coordinates of the body in space, you can find it velocity and acceleration in each coordinate space.

Instruction

1. Find the increment of the function: Δf = f(x0+Δx) - f(x0). Find the ratio of the increment function to increment of argument: Δf/Δx = (f(x0+Δx) - f(x0))/Δx. It is assumed that Δx tends to zero. This will be the derivative of function at point x0. In practice, first find a General formula for the derivative function and then substitute the specific value of the argument.
2. For example, f(x) = x^3 - 2x^2 + x + 1, we need to find the derivative at point x = 4.
   Find the derivative f(x) = 3x^2 - 2*2x + 1. Find the derivative of f'(4) = 3*4^2 - 4*4 + 1 = 48 - 16 + 1 = 33.