Using Newton's theory to introduce calculus is a bit like using a hammer to crack a nut.
This does both Newton and the student a disservice - so is there a better way?
A graph by John Wallis showing the area above and below the curve gave me a clue.
I discovered a simple relation between these two areas and the power of 'x'.
This relation is used in Power Maths to deduce the integral power rule.
An even simpler relation is used to deduce the differential power rule.
Click on the 'Introduction' button to see how Power Maths works.
With grateful thanks to David A Smith for his encouragement and to Lana Holden for the Java applet.
Please note: Power Maths is an introduction to, not a substitute for, the teaching of calculus.