# Math - Derivative (Sensitivity to Change)

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function or dependent variable) which is determined by another quantity (the independent variable).

What will happens to Y if I change X a little bit ? $$f(X) = Y$$ where:

The derivative measures the instantaneous rate of change of the function, as distinct from its average rate of change.

## 3 - Example

The derivative of the position of a moving object with respect to time is the object's velocity. This measures how quickly the position of the object changes when time is advanced.

## 4 - Formula

The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value.

In fact, the derivative at a point of a function of a single variable is:

• the slope
• of the tangent line

to the graph of the function at that point.