When we are forced to derive something like:
dy 9x2
dx 3x
We could divide this out or re-write it to allow us to use the product rule, but the simplest way is to use what is called the quotient rule:
(f/g)'(x) = g(x)f'(x)-f(x)g'(x)
(g(x))2
All this means is that we
{(multiply the
denominator with the derivative of the
numerator), subtract the product of (the
numerator and the
derivative of the denominator)
} and divide all this mess by the
{square of the denominator
}.