If y = (1+3x)^2, what is dy/dx?

A good approach to solve this is to use the chain rule of differentiation. The chain rule states: dy/dx= (dy/du)*(du/dx).

In this case let u = 1+3x, so y = u^2.

Then dy/du = 2u and du/dx = 3,

so dy/dx = (2u)*3 = (2(1+3x))*3 = 6+18x