The power rule is a quick means of finding the

derivative of a

function. To apply the

power rule, take the

exponent and make it the new

coefficient of the

derivative. Now decrement the

exponent by one. The resulting function is the derivative of the original function.

__Example__
f(x) = x

^{2}
f

^{1} (x) = 2x

^{2-1}
f

^{1} (x) = 2x

^{1}
f

^{1} (x) = 2x

If the

variable has a

coefficient, the

power rule is applied to the

exponent and variable in the above manner and then multiplied by that coefficient, as follows:

f(x) = 4x

^{3}
f

^{1} (x) = 4 * (3x

^{2})

f

^{1} (x) = 12x

^{2}