How can I solve this implicit differentiation problem?

[dankelly08]

so I have a implicit diffentiation problem and was wondering if someone could help me out.. I need to figure out how to get

dy/dx=0

so eg if i had

dy/dx = 4xy+2x/5y^2

and you want to write this in terms of y, how is this done? is there a trick?

 

[arildno]

Well, if dy/dx is to be 0, it follows that:
$$x(4y+\frac{2}{5y^{2}})=0$$
Having as possible solutions that either x=0, or $$y=-\frac{1}{\sqrt[3]{10}}$$

 

[dankelly08]

thanks for your help, but I am still not too sure how this works so how about with this example

1-2x/4+2y = 0

 

[arildno]

Well, then along the line y=x/4-1/2, dy/dx will equal zero.

 

[dankelly08]

ah right thanks, its just I'm trying to figure out in my notes what steps my lecturer took to get x=1/2.. and i can't see how he's done it..