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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.


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