# Implicit differentiation

1. Apr 17, 2007

### t_n_p

1. The problem statement, all variables and given/known data

2. Relevant equations

3. 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!

2. Apr 17, 2007

### 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.

3. Apr 17, 2007

### HallsofIvy

Staff Emeritus
Rather than writing $\sqrt{xy}$ as (xy)1/2, write it as x1/2y1/2. I think you will find that less confusing.

4. Apr 17, 2007

### t_n_p

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!

5. Apr 17, 2007

### daveb

Yes, you're on the right track now!

6. Apr 17, 2007