Instead of doing implicit differentiation, can you solve for y and then take the derivative?

Question

anonymous · Answer

for example, 2 - 8xy = 5x - 3y
3y -8xy = 5x - 2
y = (5x-2) / (3-8x),
dy/dx = 5(3-8x) - (-8)(5x-2) / (3-8x)^2

hero · Answer

You can, but only when you are able to solve for y. You cannot with functions where you are not able to solve for y

anonymous · Answer

This is right I think...

anonymous · Answer

what is an example of a function you cannot solve for y?

hero · Answer

$$x^2 - 2y^3 +4y = 2$$

anonymous · Answer

so functions like this must have y on the other side of dy/dx

anonymous · Answer

so you need implicit differentiation because sometimes you cannot single out the y?

hero · Answer

Precisely

anonymous · Answer

and most of the time, you cannot solve for y because they are not functions...