# Math - Derivative (Sensitivity to Change, Differentiation)

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.

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.

## Example

Made with the Math.js library that implements this Differentiation rules for computing the derivative of a function in calculus.

console.log('calculate derivatives');
console.log(math.derivative('2x^2 + 3x + 4', 'x').toString());  // '4 * x + 3'
console.log(math.derivative('sin(2x)', 'x').toString());        // '2 * cos(2 * x)'


## 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.