[Callum]

I'm trying to do some last-minute math revision, as I have a test on Monday, and I found a question I can't do. And the mark-scheme doesn't make sense.

The question:

f:x |-> 3^x

Find the solution of the equation f''(x) = 2

My first step was to find the inverse of f(x)... f'(x)

So I let k = 3^x
ln(k) = ln(3^x)
ln(k) = x(ln(3))
x = (ln(k))/(ln3)
(x = log(base 3)(k))

But then I tried finding the inverse of the inverse... f''(x)and got the original function.

The answer scheme, however, says that f'(x) is not what I got at all, but is actually (3^x)(ln(3)).

What am I doing wrong?