Simple multivariable problem w/ ellipse

[MeMoses]

Homework Statement

If u=x^3 + 3xy + y^3, determine du/dx on the ellipse 2x^2+3y^2=1

2. The attempt at a solution

Imagine I just use partial derivative somehow, but I'm not sure what the question is asking by on the ellipse. I have a feeling its just something simple that I'm overlooking. Any help is appreciated. Thanks

 

[HallsofIvy]

The chain rule:
$$\frac{du}{dx}= \frac{\partial u}{\partial x}+ \frac{\partial u}{\partial y}\frac{dy}{dx}$$
You get dy/dx from the requirement that $2x^2+ 3y^2= 1$, of course.