Well, firstly write down the Newton quotient (f(x+h)-f(x))/h. The derivative is going to be the limit of this as h -> 0. In this case f(x) = 1/sqrt(x), so the NQ is [1/sqrt(x+h) - 1/sqrt(x)]/h Now put over a common denominator as [sqrt(x) - sqrt(x+h)]/[h.sqrt(x).sqrt(x+h)]. Multiply top and bottom by sqrt(x)+sqrt(x+h) and you have [x - (x+h)]/[h.sqrt(x).sqrt(x+h).{sqrt(x)+sqrt(x+h)}] and this simplifies to -1/[sqrt(x).sqrt(x+h).{sqrt(x)+sqrt(x+h)}]. Now you can let h->0.