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Mathematics 13 Online
OpenStudy (anonymous):

Calculas

OpenStudy (anonymous):

bring it :)

OpenStudy (anonymous):

Find dy/dx by implicit Differentiation \[\sqrt{xy} = x-2y\]

OpenStudy (anonymous):

square both sides then solve dy/dx of xy=x^2-4xy+4y^2

OpenStudy (anonymous):

let me know if you need further help

OpenStudy (anonymous):

so left side will equal 1y'=.....

OpenStudy (anonymous):

How do I get dy/dx?

OpenStudy (anonymous):

I tried using the chain rule but Im pretty sure Im doing it wrong.

OpenStudy (anonymous):

you could do it this way: as you should know, \(y'(x)=-\large\frac{F_x}{F_y}\) where \(F(x,y)=x-2y-\sqrt{xy}\) So: \(F_x=1-\large\frac{y}{\sqrt{xy}}\) and \(F_y=-2-\large\frac{x}{\sqrt{xy}}\) now just find the quotient with oposite sign and you got your answer.

OpenStudy (anonymous):

In previous post I forgot 2 in the denominator in expretions of F_x and F_y, as probably you noticed. other way: differentiating iplicitly: \(\large\frac{xy'+y}{2\sqrt{xy}}=1-2y'\) express y' from here to get the answer

OpenStudy (isaiah.feynman):

So we're finding y prime right?

OpenStudy (anonymous):

Yes sir..

OpenStudy (isaiah.feynman):

\[y' = \frac{ xy^{2} }{-4-2x } - \frac{ 1 }{ -2-x }\]That's what I got.

OpenStudy (anonymous):

Can you draw it please?

OpenStudy (isaiah.feynman):

I think I need others to check it as well.

OpenStudy (isaiah.feynman):

I'm wrong. I just saw an error.

OpenStudy (anonymous):

Yeah, I dont think thats the answer. I tried Myko's solution, I still dont think I did it right.

OpenStudy (anonymous):

Oh haha okay

OpenStudy (isaiah.feynman):

But I will solve it correctly!

OpenStudy (anonymous):

Its okay you really dont need to. I'm failing calculas anyway.

OpenStudy (isaiah.feynman):

Lol.I remember I started doing well after the first midterm.

OpenStudy (anonymous):

Are you serious? My AP exam is after the midterms

OpenStudy (isaiah.feynman):

What's AP?

OpenStudy (anonymous):

Its an exam we have to take if we are taking a college level class.

OpenStudy (isaiah.feynman):

I think I got it right

OpenStudy (isaiah.feynman):

\[y' = \frac{ 2\sqrt{xy}-y }{x+4\sqrt{xy}} \]

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