Are you sure you copied the right problem?
Hello all,
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.
You seem to have arrived at the same thing as me - the last term would appear to yield a term in x^12 when the substitution for y is used. This is a copy paste from the actual question on the website (i'd link you but you need a university account to get in):
Given that u = x5 -10x3y2 + 5xy4, and y = 1 + x2, show that
du
dx= 5 + 30x2 + 55x4 + 70x6 + 45x8
The formatting isn't perfect but you can see what they think the answer is.