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...
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...