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

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Answer 1 · 2015-11-11T04:56:24

See the explanation section below.

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-3))/(h(sqrt(x+h-3)+sqrt(x-3))#

# = 1/(sqrt(x+h-3)+sqrt(x-3))#