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Home Differentiation Inverse Functions Power Rule for Rational Exponents
 
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Power Rule for Rational Exponents

POWER RULE FOR RATIONAL EXPONENTS

Let y = xr where r is a rational number. Then whenever x > 0,

02_differentiation-241.gif

PROOF Let r = m/n where m and n are integers, n > 0. Let

u = x1/n, y = um.

Then

02_differentiation-242.gif

and

02_differentiation-243.gif
Home Differentiation Inverse Functions Power Rule for Rational Exponents

Last Update: 2006-11-05