Using the limit definition, how do you differentiate f(x) =sqrt(x−3)f(x)=√x−3?

1 Answer
Jim H
Nov 11, 2015

See the explanation section below.

Explanation:

The crucial step is to use the following to remove the square roots from the numerator.

(sqrt(x+h-3)-sqrt(x-3))/h = ((sqrt(x+h-3)-sqrt(x-3)))/h ((sqrt(x+h-3)+sqrt(x-3)))/((sqrt(x+h-3)+sqrt(x-3)))√x+h−3−√x−3h=(√x+h−3−√x−3)h(√x+h−3+√x−3)(√x+h−3+√x−3)

= (x+h-3-(x-3))/(h(sqrt(x+h-3)+sqrt(x-3))=x+h−3−(x−3)h(√x+h−3+√x−3)

= 1/(sqrt(x+h-3)+sqrt(x-3))=1√x+h−3+√x−3

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