Find dy/dx and d^2y/dx^2 as functions of x and y given that xy^2+y=1. Thank you
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did you try doing it?
I did yes.. a poor attempt. xy^2+y=1 d/dx[xy^2+y] y^2dy/dx+y dy/dx=-y/y^2 dy/dx=-1/y
Originally Posted by lyoung I did yes.. a poor attempt. xy^2+y=1 d/dx[xy^2+y] y^2dy/dx+y dy/dx=-y/y^2 dy/dx=-1/y You did the derivative of the first term wrong. And you never took the derivative of the last term on the LHS. d/dx(xy^2 + y) = y^2 + 2xy*y' + y' -Dan
Where does the +y' come from? Is it not a negative?
Originally Posted by lyoung Where does the +y' come from? Is it not a negative? If you multiply out the LHS side of Dan's line in post 4 before differentiating you get d/dx(xy^2) + d/dx(y). Now differentiate this and you will get the RHS of Dan's post 4.
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