Which rules to use (Product rule?)

[BOAS]

Homework Statement

Find the gradient of the curve at the given point on the curve

y = \frac{(√x - 1)}{√x} where x = 9

Homework Equations

y(x) = u(x)v(x)

dy/dx = u(dv/dx) + v(du/dx)

The Attempt at a Solution

my problem really boils down to rearranging the function to a form easy to manipulate so i'll show you how far I get and where I think I'm going wrong.

y = \frac{(√x - 1)}{√x}

y = (x^1/2-1)x^-1/2

Here, I'm not sure whether the first bracket should read (x^1/2-1) or (x-1)^1/2.

Treating it as y = (x^1/2-1)x^-1/2 I can apply the product rule easily enough, but if I were to expand out those brackets I get y =1 - x^{-1/2} which when I put into a graphing program is slightly different to the original...

I'm pretty sure I've treated the brackets in the original equation wrong with respect to the square root.

If you could help clear this up for me, that would be great!

 

[FeDeX_LaTeX]

You need only use the power rule here. Do you see why?