Chain Rule - Book Example
I am having trouble understanding a portion of the textbook example. It's seems to be mostly with the simplifing of the answer.
Find dy/dx if y = u^3 - 3u^2 + 1 and u = x^2 + 2
dy/du = 3u^2 - 6u and du/dx = 2x
it follows that dx/dy = (3u^2 - 6u)(2x). *I'm fine so far, keep going*
We are substituting x^2 + 2 for u in the expression for dy/dx giving
[3(x^2+2)^2 - 6(x^2+2)](2x)
*I understand everything above but the next step confuses me*
I don't know what steps they took to arrive at that equation. Could you possible show me the 'longer' process?
It goes on to give: