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# Implicit Differentiation question watch

1. Ive got a question that I just can't seem to get the answer to:
find dy/dx of

The final answer is but I am not entirely sure on how to get to this stage.

My attempt:
I think I worked the derivative of
to be
The derivative of
to be (obviously)
And finally
to be
2. Move the sin(x) term to the RHS (its easier to deal then with factorising the y ' (x) terms)

differentiate the entire thing, so you get:

then multiply the entire equation by:

and see where that gets you..

(ooh, and factor out the y' on the LHS, moving the 1st term in the 1st line above to the RHS)

(EDITED)
3. I've tried it again, using methods that you showed and have ended up with (-y-2cos(x)(xy)^1/2) / (-2((xy)^1/2) sin(y)-x)
Apologies, LaTex isn't working for some reason.
4. your answer is correct apart from a minus sign infront of 2root(x)root(y) in the denominator (maybe a small mistake somewhere) - just take a factor of -1 out from the numerator in the answer you gave, THEIR numerator is incorrect as it doesnt have the root(xy) term (the root(cos(x) term is wrong also)
5. That's how I'll deal with all problems in the future. If my answer doesn't match theirs, their answer is wrong! :P But seriously, I think you're right, I see no possible way of getting root cos anywhere in that equation. Thanks for the help!

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Updated: January 28, 2015
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