You haven't done anything wrong, you just need to combine the terms of your answer.
Question is:
y = (x + 1) \sqrt[x - 1]
So I convert to
y = (x + 1) (x - 1)^(1/2)
Then
dy/dx = (x -1)^(1/2) . 1 + (x + 1) 1/2(x - 1)^(-1/2) . 1
y= (x - 1)^{1/2} + \frac{(x + 1}{2(x - 1)^{\frac{1}{2}}}
Is this correct?
Book says numerator is 3x - 1!
What have I done wrong?
Angus
I did struggle with the rationalising. I was thinking
\sqrt{x-1} * \sqrt{x-1}
would be multiplied like (x - 1)(x - 1) - ie x * x, x * -1 etc, but of course it is not. you just add the powers. ie (x - 1)^(1/2) (x - 1)^(1/2) = (x - 1)
Sorry I will learn how to do latex some time. I put around [tex] tags but it doesn't work for me.