Let $f(x)=-\frac{6}{x}$. Then according to the definition of derivative

 $f^\prime(x)= \displaystyle \lim_{h\to 0}$ ------------------------------------------------

(Your answer above and the next few answers below will involve the variables $x$ and $h$. We are using h instead of $\Delta x$ because it is easier to type)
We can cancel the common factor from the numerator and denominator leaving the polynomial

Taking the limit of this expression gives us $f'(x) =$