How do I differentiate a square root?

ebaines · Mar 19, 2012, 10:48 AM

You are correct. Another way to do this is to use the formula for derivate of a fraction:

$ (\frac {f(x)}{g(x)} )' = \frac { g(x) f'(x) - f(x)g'(x)} {g(x))^2} $

For this problem this gives:

$ \frac {2x(\sqrt x + 1) \frac 1 2 x^{-1/2} - (\sqrt x +1)^2} {x^2} = \frac {x + \sqrt x -(x + 2 \sqrt x +1)} {x^2} = -x^{-3/2} -x^{-2} $

which is the same answer you got.

However, if you integrate the answer that the answer sheet gives it turns out to be the derivative of (x sqrt(x) +1)^2/x^2. So could there have been a mistake in the original question as you typed it on this site?

AdrianCavinder · Mar 22, 2012, 08:18 PM

Dear Uber, Thanks so much. Very helpful.

How do I differentiate a square root?

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