I have a problem which I can not seem to fathom. I am asked to differentiate [(sqrt x) + 1]^2 / x with respect to x. I tackled the problem as follows:
First I expanded the top term to become [x + 2(sqrt x) + 1]. Then I multiplied by x^-1 to get 1 + 2(sqrt x)^-1 + x^-1.
When I differentiated, I got -x^-3/2 - x^-2, but the answer sheet says 1 - x^-3/2 - 2x^-3. I can not see where I am going wrong. Any help would be appreciated. Cheers. Adrian.