Explanation

For many functions the rate of change changes depending on the X value.

Graphically this can be seen by drawing a tangent to the curve at that point can be drawn by drawing a line between two points on the curve where one is drawn at a slightly lower x value than the point in question and the other slightly higher x value than the point in question.

From the differences in x and y coordinates of these two points the gradient can be obtained of the tangent at that mid point. The closer these points either side of the point being examined the more accurate the gradient.

There are a number of rules from which the gradient of the tangent can be obtained.

This tool allows the user to enter the equation of a functions, click to reveal the derivative of the function and by dragging the white dot move the being investigated.

Note when entering the equation you may find it easier to enter powers using the caret symbol ^ above the 6 on most keyboards followed by a power.