Finding dy/dx of equation using both chain rule and product rule

Hello everyone,

Recently I've been learning about the chain rule and the product rule, which by themselves is fairly straightforward to solve. However, it becomes a little more complex when attempting to solve an equation with both of them together. So any help in solving the following equation using the chain rule and product rule will be greatly appreciated. :)

Here is the equation:

y = (3x + 5) ^2 x (2x - 2)

I solved the chain rule part (I think), which is the (3x + 5) ^2 segment. Using the chain rule, I got the answer 6(3x + 5), leaving me with the equation of:

y = 6(3x + 5)(2x - 2) to be solved using the product rule. But I am not entirely confident with the steps involved, as I believe it involves factorizing and such.

Thanks!

Nathaniel