Derivatives of Power Functions

Example:

y = x^-1/4

To take the derivative of this function we notice that it is a power function, because the independent variable is in the denominator and the exponent is constant:

^-1/4

The Power Rule (Derivative Rule for Power Functions):

The derivative of any power function is the product of its exponent and a power function with the exponent decreased by one.
If

xⁿ

then the derivative of z is

z '

n x^n-1

So our example,

^-1/4

Must have as its derivative

y '	=	-1/4	x	^{-1/4 - 1}
	=	(-1/4)*x^-5/4

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glarose@umich.edu
©2001 Gavin LaRose, University of Michigan Math Dept.