Hello, Im currently taking a course in economics at master level and I have a question regarding how you get to the final point in the slides I attach to this post.
I have basic knowledge of differentiation but even when googling around I cant seem to grasp how to get to the final result in the bottom. Summing up what I know about the problem:
In the indifference curve the C(L) (consumption as a function of leisure)
C'(L) is equal to (-1)* (The utility function differentiated wrt L divided by The utility function differentiated wrt L) or in other words = - (UL/UC)
I know that the quotient rule for differentiation is supposed to be used, so if Z=X/Y then Z'= (X'Y - XY'/(Y^2) so for my problem it should probably be C''(L)=(UL'UC - ULUC'/((UC)^2) and that some implicit derivation should be used to get to the final result.
Does anyone know the rules used? I cant seem to apply the rules to this problem of using the rules on already differentiated variables.
Thanks in advance!
Over the Easter break