# More Differentiation Questions

• Dec 10th 2008, 06:06 PM
timmy420
More Differentiation Questions
I guess i should first ask, is it proper form here to start new threads or edit my old ones... either way, i'll post in this new one for now.

Trying to work out y' of the square root of x-1 / x+1 (all terms inside the root, didnt know how to indicate that in text)

I assume that I make it (x-1 / x+1)^1/2 but i get into a very tangly equation when I use the quotient rule. Is this the right way to start here?
• Dec 10th 2008, 06:14 PM
tester85
Have to use chain rule and quotient rule.

y = sqrt(x-1 / x+1)
y = (x-1 / x+1)^0.5
dy/dx = 0.5(x-1 / x+1)^-0.5 multiply d/dx(x-1/x+1)

Can you take it from here ?

Quote:

Originally Posted by timmy420
I guess i should first ask, is it proper form here to start new threads or edit my old ones... either way, i'll post in this new one for now.

Trying to work out y' of the square root of x-1 / x+1 (all terms inside the root, didnt know how to indicate that in text)

I assume that I make it (x-1 / x+1)^1/2 but i get into a very tangly equation when I use the quotient rule. Is this the right way to start here?

• Dec 10th 2008, 07:54 PM
timmy420
i got the chain rule part, but im getting tangled up in the algebra i think.

I multiply .5(x-1/x+1)^.5 by the derrivitive which i worked out to be 2/(x+1)^2 and get confused.
• Dec 10th 2008, 08:52 PM
tester85
y = sqrt(x-1 / x+1)
y = (x-1 / x+1)^0.5
dy/dx = 0.5(x-1 / x+1)^-0.5 multiply d/dx(x-1/x+1)
dy/dx = 1/2(x-1 / x+1)^-1/2 multiply ((x+1)(1) - (x-1)(1) / (x+1)^2)
dy/dx = 1/2(sqrt(x+1)/sqrt(x-1)) multiply 2 / (x+1)^2
dy/dx = sqrt(x+1)/sqrt(x-1)(x+1)^2
• Dec 10th 2008, 09:08 PM
Msquared
You can always use synthetic or long division to reduce the equation inside the radical to:

1- (2)/(x+1)

Makes it a little more bearable to derive and you no longer have to worry about applying the quotient rule to the interior of the radical.