Derivatives Graphs

by M. Bourne

Interactive Graph showing Differentiation of a Polynomial Function

In the following interactive you can explore how the slope of a curve changes as the variable `x` changes.

Things to do

  1. Drag the point P left and right to see how the slope of the tangent varies as `x` varies. (Keep your mouse cursor over the graph. A left-right motion works better than up-down.)
  2. Select the "show the graph of derivative" which gives you the derivative function. Then once again, drag point P left and right and observe how the 2 curves are related.
  3. Choose one of the other 2 curves and explore its slope.

The height of the right triangle (with P at one vertex) indicates the slope. It has a base of 1 unit.

Copyright ©


Here are the derivatives of the 3 functions given above:

1. Quadratic (parabola), `y=x^2-10x-1`.

Derivative: `dy/dx=2x-10`

2. Cubic, `y=0.015x^3-0.25x^2+0.49x+0.47`.

Derivative: `dy/dx=0.045x^2-0.5x+0.49`

3. Quartic `y=x^4-1.5x^3-6x^2+3.5x+3`.

Derivative: `dy/dx= 4x^3-4.5x^2-12x+3.5`

See how to find these derivatives in the Derivatives of Polynomials section.


Graph developed using JSXGraph.


Search IntMath, blog and Forum

Online Algebra Solver

This algebra solver can solve a wide range of math problems.

Calculus Lessons on DVD


Easy to understand calculus lessons on DVD. See samples before you commit.

More info: Calculus videos

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.