Differentiate both sides of the given equation directly.
If y^(1/2)=x/[(xy^(1/2)+y], find dy/dx.

Question

Differentiate both sides of the given equation directly.
If y^(1/2)=x/[(xy^(1/2)+y], find dy/dx.

anonymous · Answer

Implicit differentiation?  Were you able to start the problem?

anonymous · Answer

You want to treat y as a function of x...   
so d/dx of y  is y' 
and d/dx of some function of y (like y^2 for example) requires the chain rule:
d/dx (y^2) = 2*y*y'

anonymous · Answer

(((([xy^(1/2)+y]^2/2y^(1/2) + x{x/[2y^(1/2) +1]} ))))(dy/dx) = y
i dont know what to do next.

anonymous · Answer

trying to read that...

anonymous · Answer

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anonymous · Answer

ans is 2(1-y)/[2x+3y^(1/2)]
i have no idea how to do this.

anonymous · Answer

well,  it looks like you're on the right track...  just divide by the coeffecient of dy/dx and you should be done.

anonymous · Answer

It's almost impossible to read what you've got there, so I'll try to rewrite it... tell me if I'm right.

anonymous · Answer

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