Differentiate y = (3x^2 + 1)^2

Looking at this question the first thing we should notice is that there is a an x squared inside a bracket which is also squared. As there is function inside a function we must use the chain rule. The simple way to think about applying the chain rule in this case is to 'differentiate the outside' and times that by what you get when you 'differentiate the inside'. So first of all we differentiate the bracket meaning we times the whole thing by 2 (because the bracket is to the power of 2) then take 1 off the power meaning we get 2(3x^2 + 1)^2-1 = 2(3x^2 + 1). Differentiating the inside means differentiating the function 3x^2 + 1. To do this we times 3x^2 by 2 (as the x is to the power 2) and minus 1 from the power to get 6x. As the one is a constant, when differentiated this becomes 0. To apply the chain rule we must times both of these together: 2(3x^2 + 1) * 6x = 12x(3x^2 + 1). That is your final answer