A question about total differentiation is doing my head in. It is:

u = x^5 - 10x^3y^2 + 5xy^4 and y = 1 + x^2

It wants me to show that du/dx is some expression in x involving x's up to the power 8. But my technique gives rise to x's up to the power 12. I've been using du = (partial du/dx)dx + (partial du/dy)dy, and dividing through by dx, leaving du/dx on the left and then multiples of dx/dx (=1) and dy/dx (=2x) on the right.

Am I doing this wrong? Any help appreciated.