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

We have to use the chain rule here. If we set u to the inside of the bracket, u = x^2 + 3 and differentiating we get du/dx = 2x. Now the original expression becomes y = u^2. Differentiating this with respect to x, dy/dx = du/dx * dy/du using the chain rule. dy/du = 2u and du/dx is 2x so the final answer dy/dx = 2x*2(x^2 + 3) = 4x(x^2 + 3).