Derivatives of Power Functions

Example:

y = t^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	t	^{1/4 - 1}
	=	(1/4)*t^-3/4

practice gateway test
previous page

Page Generated: Thu Jan 1 00:17:02 2026
Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose, University of Michigan Math Dept.