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Home Q & A Board Science-Related Homework Help Mathematics Calculus
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Rellias Minn Rellias Minn
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2 months ago
Solve for the y′ of the given implicit functions (Based from the example).
1. \(3y^2\left(x+y\right)=x-y\)

Example:
\(\left(x+y\right)^2=3xy\)

\(2\left(x+y\right)\left(dx+dy\right)=3\left(xdy+ydx\right)\)

\(2\left(xdx+xdy+ydx+ydy\right)=3xdy+3ydx\)

\(2xdy+2ydy-3xdy=3ydx-2xdx-2ydx\)

\(dy\left(2y-x\right)=dx\left(y-2x\right)\)

\(\frac{dy}{dx}=y'=\frac{y-2x}{2y-x}\)
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Rellias M. Author
wrote...
#1
2 months ago
Umm... I don't quite understand how would I multiply 3y^2 and (x+y) in order for it to factor out the dx because it conflicts with my solution if I try to solve it
wrote...
#2
Educator
2 months ago
I believe it is done like this:
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