Derivatives of Power Functions

Example:
y = t4

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 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 4
Must have as its derivative
y ' = 4 t 4 - 1
  = 4*t3
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©2001 Gavin LaRose, University of Michigan Math Dept.