I have been reading a book called Introduction to Modern Economic Growth by Daron Acemoglu. Up until now, the mathematics had been within my understanding. However, I found a proof which baffles my understanding. It requires the use of the Implicit Function Theorem. I tried doing it in many ways, but I could not connect the two ends. Can someone at least give me a hint as to how this is possible? I am getting a completely different expression for the partial derivative of k*(s).
Sorry, I got it just now. It uses u/v rule of differentiation with the Implicit theorem being a very small part of the proof.