Question

If y= (2x + 2)^3 find dy/dx using chains rule

Answer 1

Just use the power rule and the chain rule.

y = u^n
dy/dx = n u^(n-1) du/dx

Now just plug in your u=2x+2 and crank it out.

I might even go ahead and simplify it to

y = 2^3 (x+1)^3 = 8(x+1)^3
Then du/dx = 1

Answer 2

I would just do it in one step

dy/dx = 2(2x+3)^2 (2)
= 4(2x+3)^2

using the steps asked for:
let u = 2x+2
du/dx = 2
then y = u^3
dy/du = 3u^2

dy/dx = (dy/du)(du/dx) = (3u^2)(2)
= 4u^2
= 4(2x+2)^2

Once you see the pattern of these type of derivatives, you should be able to differentiate using the simple approach I used at the top.