Derivatives of Power Functions

Example:
y = s5

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:

y = s 5

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
  z = xn
then the derivative of z is
  z ' = n xn-1

So our example,

y = s 5
Must have as its derivative
y ' = 5 s 5 - 1
  = 5*s4
[]

practice gateway test
previous page
Page Generated: Fri Jun 6 01:34:03 2025
Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose, University of Michigan Math Dept.