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:

y = t -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
  z = xn
then the derivative of z is
  z ' = n xn-1

So our example,

y = t -1/4
Must have as its derivative
y ' = -1/4 t -1/4 - 1
  = (-1/4)*t-5/4
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©2001 Gavin LaRose, University of Michigan Math Dept.