De afgeleide als functie

The derivative measures how the dependent variable changes with respect to the independent variable.

Graphically, the derivative is the limit of the average rate of change as the interval approaches zero.

In mathematical terms, the derivative function, f′(x), assigns a slope to each point on the graph of f(x) —showing how the output changes in response to changes in the input.

When calculated at every point in a function’s domain, it produces a new function—the derivative function.

For instance, at point A, the graph of f(x) is decreasing, and the tangent line has a negative slope. So, the derivative f'(x) takes on a negative value at this point, corresponding to the point A on the graph of f(x).

At point B, the tangent is horizontal or the slope is zero, which means the derivative function is zero. At point C, the slope is positive, shown by a positive value of the derivative function.

As a result, the derivative function shows how rapidly the original function is changing at each point.

One example of a derivative is found in motion, where the derivative of a car’s velocity with respect to time gives an acceleration function.