Using the limit definition, how do you find the derivative of f(x) = sqrt(x + 2)f(x)=√x+2?

1 Answer
Jim G.
May 6, 2018

f'(x)=1/(2sqrt(x+2))

Explanation:

f'(x)=lim_(hto0)(f(x+h)-f(x))/h

=lim_(hto0)(sqrt(x+h+2)-sqrt(x+2))/h

=lim_(hto0)((sqrt(x+h+2)-sqrt(x+2))(sqrt(x+h+2)+sqrt(x+2)))/(h(sqrt(x+h+2)+sqrt(x+2))

=lim_(hto0)(x+h+2-(x+2))/(h(sqrt(x+h+2)+sqrt(x+2))

=lim_(hto0)cancel(h)/(cancel(h)(sqrt(x+h+2)+sqrt(x+2)

=1/(sqrt(x+2)+sqrt(x+2))=1/(2sqrt(x+2))

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