Is My Implicit Differentiation Method Correct?

[t_n_p]

Homework Statement

http://img224.imageshack.us/img224/2459/untitledow9.jpg

Homework Equations

The Attempt at a Solution

See above picture.

I'm just curious to see if my method is correct and how exactly would I go about simplifying the answer if indeed it is correct. Thanks to anybody who can help!

 

[daveb]

Your expression for the derivative of sqrt(xy) using the chain rule is in error. Y is under the square root in the expression, so the first half should be sqrt(y/x)/2. From this you should be able to get the second half.

 

[HallsofIvy]

Rather than writing $\sqrt{xy}$ as (xy)^1/2, write it as x^1/2y^1/2. I think you will find that less confusing.

 

[t_n_p]

http://img149.imageshack.us/img149/9232/workingdh2.jpg

Thanks for pointing that out, I made the relevant changes, I hope it's a bit better now. The final answer seems very, very long winded though. Am I on the right track? Hope nobody minds me posting the pictures instead, it's easier for me than doing it on the computer!

 

[daveb]

Yes, you're on the right track now!

 

[t_n_p]

thanks for speed reply
My final answer is...

http://img413.imageshack.us/img413/246/finalanswml7.jpg

amiright?