# Derivatives Graphs

by M. Bourne

## Interactive Graph showing Differentiation of a Function

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

### Things to do

**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.)**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.**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.

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## Background

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`

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

3. Quotient `y=(4x^2)/(x^3+3)`.

Derivative: `dy/dx=(-4x^4+24x)/((x^3+3)^2)`

We saw how tp find this derivative in the last example of the Derivatives of Products and Quotients section.

### Credits

JSXGraph by: A "small team" at the University of Bayreuth, Germany.

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