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Title: Use Implicit Differentiation to solve this function Post by: Rellias Minn on Jan 27, 2023 Solve for the y′ of the given implicit functions (Based from the example).
1. \(3y^2\left(x+y\right)=x-y\) Example: \(\left(x+y\right)^2=3xy\) \(2\left(x+y\right)\left(dx+dy\right)=3\left(xdy+ydx\right)\) \(2\left(xdx+xdy+ydx+ydy\right)=3xdy+3ydx\) \(2xdy+2ydy-3xdy=3ydx-2xdx-2ydx\) \(dy\left(2y-x\right)=dx\left(y-2x\right)\) \(\frac{dy}{dx}=y'=\frac{y-2x}{2y-x}\) Title: Re: Use Implicit Differentiation to solve this function Post by: Rellias Minn on Jan 27, 2023 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
Title: Re: Use Implicit Differentiation to solve this function Post by: bio_man on Jan 27, 2023 I believe it is done like this:
(https://biology-forums.com/gallery/46/6_27_01_23_9_11_28.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=46118) |