Math - Derivative (Sensitivity to Change, Differentiation)

About

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 ? <MATH> f(X) = Y </MATH> 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.

Documentation / Reference


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