Langara College - Department of Mathematics and Statistics
Internet Resources for the Calculus Student
Power Rule for Derivatives
d/dx(x^p) = p*x^(p-1)
This can be proved by going back to the definition
and using either the Binomial
Theorem or a difference of powers factorization to simplify the difference
quotient. (It can also be proved by using the Product
Rule and Mathematical
Induction. )
By combining this with the Sum and Constant Multiple rules you can quickly
write down the derivative of any polynomial.
The IES group in Japan have an applet giving a graphical
illustration of a family of Cubics and their derivatives (This does
not actually show the formulas involved, but does illustrate why it is
plausible for the derivative of a cubic to always be a quadratic.)
You might also check our 'raw
list' (of links provided without comment) to see if there are any more
examples there that we haven't yet included here.
If you have come across any good web-based illustrations of the power
rule,
please do let
us know and we will add them here.