This is a problem we did previously on a test; my answer was marked correct, but I am having trouble getting my answer in the same form that my teacher gave it.

Question

The question:
Find the derivative of (x/(x+1))^1/2

His answer: ( (x(x+1))^(1/2) ) / (2x(x+1)^2)

My answer: ((x+1)^(1/2)) / 2((x)^(1/2))((x+1)^2)

It looks to me like his answer is just my answer multiplied by x^(1/2) on the top and bottom, but I don't know how he did that. I'd like to know how to get my answer into the same form as his, because he asked us (as extra credit) to do the same problem using another method, and it would be easier for me to compare answers if mine was in the form he provided.

Any help would be welcome.

Answer 1

Never mind, I figured it out-- he rationalized the denominator.