The image is pretty much self-explanatory. To add some context, I'm learning Solow-Swan Growth Theory and my professor said that the marginal product will not change if both capital and labor increase at the same scale.
I can intuitively understand that it makes sense but trying to apply a simple equation (the blue one, the definition of constant marginal product) is just not working.
It's either I'm not partial differentiating correctly or the whole theory is wrong.
I don't see anything wrong with what I've done but why are they not the same?