I have a tricky implicit differentiation problem I can't seem to get my head around.
Define the function L as follows, let's call this equation 1:
L(a) = ( ( c - a ) / a ) X
And define a* as the value of a which solves the following expression, let's call this equation 2:
( 1 - L(a*) ) ( a*) = g
Now I am trying to calculate da* / dX which is done by differentiating both sides of equation 2. I cannot get a solution to this. My source of confusion stems from the fact that L is a function of both a* and X. Can anybody give me some guidance to this problem? Any help would be enormously appreciated. Thanks!