Help Please! How to explain these differences mathematically?

[hatali]

I solved it and marked the part that needed to be explained. I see how TC’(Q)/Q is similar but different to d/dQ[TC(Q)/Q] but I don’t know how to explain it mathematically. Please help!

 

[Dr.Peterson]

What is your difficulty? I don't understand what you are asking for help with.

Of course they aren't the same (you'd need the quotient rule to find d/dQ[TC(Q)/Q] directly); and I wouldn't call them "similar".

 

[Steven G]

I too would not call them similar.

However it is an interesting question to find all functions such that f'(x)/x = (f(x)/x).