Deriving the first order condition (using the product rule?)

[Guest]

Hi there, I need help with the following:

A profit function if given by:

Screenshot 2020-04-26 at 3.35.39 PM.png (4.69 KiB) Viewed 311 times

I need help (preferably with steps) to prove the the first order condition is:

Screenshot 2020-04-26 at 3.38.11 PM.png (6.93 KiB) Viewed 311 times

Thanks.

[Guest]

Okay, since you are referring to the derivative can we assume that you have taken at least an introductory course in Calculus? If you have then you should know some basic derivative rules such as that the derivative of 2+ l1+ l2 with respect to l1 is 1, the derivative of -2- 3l1+ 2l2 with respect to l1 is -3, and the derivative of Cfg, where C is a constant f is a function if l1 and possibly other variables, g is a function of l1 and possibly other variables, with respect to l1 is C times the derivative of f times g plus C times f times the derivative of g: Cf'g+ Cfg'.