Question

find dy/dx=cube root (y)

Answer 1

First, start by taking the derivative of the cube root.

From algebra, you should recognize that: \[\sqrt[3]{y} = y^\frac{ 1 }{ 3 }\]
Since this is implicit differentiation, you should be able to do the derivative of that function. Since this is a implicit derivative, you are going to multiply it by y'. If I am thinking about this right, your answer should be zero.

Answer 2

Im trying to figure out if the theorem does or does not guarentee existence, and if it does , does it or does not it not guarentee uniqueness

Answer 3

Which theorem are you referring to? Mean value?

Answer 4

Theorem for Uniqueness & Existence

Answer 5

So then you are looking for it's partial derivative then, not dy/dx.

Answer 6

First you need to find it's implicit solution. I think you can do this using separation of variables method.