Differentiate: 2(x^2+2)^3

This is a chain rule question. Unlike in ordinary differentiation we have more than just the single term 'x' with coefficient 1 raised to the power of something. e.g. x^3 Therefore, there is more steps. We can rewrite the question as 2u^3 with u=x^2+2 as this is more familiar. You can then do the differentiation in terms of u which gives you 6u^2. Now, the extra step is that we have to also differentiate the u and then multiply this by our other answer. Differentiating u gives us 2x which then multiplied by 6u^2 gives us 12x(u^2) Finally, we can now sub back in u=x^2+2 to make sure our final answer is in terms of one variable only. Therefore our final answer is, 12x((x^2+2)^2)