# Vague Partial Derivative

1. Jun 2, 2012

### lifhgrl823

Could someone please explain to me how to find the derivative of this:

dy/dx = φ(x, y)

Should I break up the equation to make it dy/dx = φ(x) + φ(y) and then derive the parts?

I would then get d²y/dx² = ∂φ/∂x + ∂φ/∂y
do I have to also multiply both terms by their respective derivatives of the inside variable?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 2, 2012

### Jorriss

If φ(x, y) is arbitrary why do you think you can break it up to φ(x) + φ(y)? If φ(x, y) = xy, how can this be broken up into φ(x) + φ(y)?

3. Jun 2, 2012

### lifhgrl823

That's a good point. My professor wrote that the second derivative should be:

∂φ/∂x + ∂φ/∂y (dy/dx) = ∂φ/∂x + φ(∂φ/∂x)

I've been trying to play around with the equation and see how I could get that answer.
All of the partial derivatives I've done previously had equations that were equal to f(x,y) or such.

4. Jun 2, 2012

### Jorriss

Can you see how the Professor gets the left side? It's the chain rule.

5. Jun 2, 2012

### algebrat

Yes, to take the second derivative of y, you should look at it as phi(x,y(x))

so partial in x with respect to first entry, plus that with respect to second entry, which requires the chain rule.