please help me I understood some of this but I want to make sure that I am doing these right. On the first one I got Q=2L+7L^2+1/3K^-2/3-4L^2/3+1/3K^-2/3

Thank you for the opportunity to help you with your question!

You have the right idea. With dQ/dK, you're taking the derivative of Q with respect to K. So in this case K is your variable and everything else is treated as a constant.

So in finding dQ/dK, we'll take the derivative term by term, remembering that K in this case is our only variable, so Q = 2KL + 7L^2 + K^1/3 - (4L^2/3 * K^1/3) becomes dQ/dK = 2L + (1/3)K^-2/3 - (4/3)*(L^2/3)*(K^-2/3).

You almost had it, you just have to remember to treat L and all values other than K as constants in this case. For example, the term 7L^2 disappears, since there is no K in the term. It would be like taking the derivative of just a constant, which is zero. So, similarly with dQ/dL:

dQ/dL = 2K + 14L - (8/3)*(L^-1/3)*(K^1/3)

Notice how in this case I treated L as the only variable and everything else as constants. I hope this helped clear things up for you.

Please let me know if you need any clarification. I'm always happy to answer your questions.