Mixed Partial Derivative

http://i.imgur.com/6RGXsiB.png

How does the highlighted red area become the highlighted blue area? I understand that (∂/∂y)(∂F/∂x) = (∂²F/∂y∂x) but what do I do with
(∂²F/∂y∂x)(dy/dx)?

Question

Mixed Partial Derivative

http://i.imgur.com/6RGXsiB.png

How does the highlighted red area become the highlighted blue area? I understand that (∂/∂y)(∂F/∂x) = (∂²F/∂y∂x) but what do I do with 
(∂²F/∂y∂x)(dy/dx)?

anonymous · Answer

dy/dx=-$F_x/F_y$

anonymous · Answer

Oh silly me,  I completely forgot about that! Thank you!