Thanks for the advice, Mr Tan.
I got the same answer but it wasn't the right answer (I am assuming that the model answer given is correct).

It does happen that model answers are incorrect. Or there was a mistake made during the proofreading and editing of the question. Post the answer - one can often work backwards to elucidate the intended question.

Hi Mr Tan, the model answer is Pi e^-a/3 (b-1).

Candice, I tried plotting the graph of f(x) on Desmos as well but obtained the expected - a horizontal line.

Candice, the model answer looks fishy. The derivative of e^f(x) always contains some expression containing x within the power, the most basic of which is e^x which is invariant after differentiation.

I tried eliminating the "b" in the denominator, but obtained another expression

f(x) = π times e^(-a/3) times e^[(b - 1) x]

which differentiates to the same expression as above, multiplied by a factor (b - 1).

In this case, the e^[(b - 1) x] remains present. Or put it simply, even the letter "x" should survive, but the model answer seems to miss out the letter "x".

Hi Mr Tan, with both Mr Eric and Mr Chau's advice. I strongly believe that the model answer given to me is incorrect. You are right :)

Thank you for your feedback and have a good day ahead.