Let [math].
Then according to the definition of derivative
[math]
(Your answer above and the next few answers below will involve the variables [math] and [math].)
The expression inside the limit simplifies to a simple fraction with
numerator [math]
and
denominator [math]
We can cancel the factor appearing in the denominator against a similar factor appearing in the numerator leaving a simpler fraction with
numerator [math]
and
denominator [math]
Taking the limit of this fractional expression gives us
[math]