dy/dx means differentiate y *with respect to x*

dy/du means differentiate y *with respect to **u*

du/dx means differentiate u *with respect to x*

y = u^{2} dy/du = 2u

u = ax + 1 du/dx = a

Since dy/du = 2u and u = ax + 1 we must have dy/du = 2(ax + 1) by simply replacing u on the right hand side by ax + 1.

So dy/du*du/dx = 2(ax + 1)*a → 2a(ax + 1) or 2a^{2}x + 2a

Notice that dy/dx = dy/du*du/dx (this is known as the chain rule) so dy/dx = 2a^{2}x + 2a.

(See http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-chain-2009-1.pdf for more information on the chain rule.)

Hope this helps!