Hi, we've recently gone over how to get the derivative of exponential and logarithmic functions, except I couldn't make it to that class and we've already moved on. I have the problem as follows:

If $10,000 is invested in a savings account offering 4% per year, compounded semiannually, how fast is the balance growing after 3 years?

Things I know:

The answer to this problem is $446.02 per year, in the back of the book.

The compound interest formula f(t) = P(1 + r/m)^mt is used.

I have to get the derivative of the formula, and then just plug in the values.

Problem is, I'm unsure how to get the derivative of the formula. I've done all I know how and I'm not getting the answer in the back.

When I tried to find the derivative this is what I came up with, please correct any errors I have made.

f '(t) = (P(1 + r/m)^mt) * ln(mt)

Any help much appreciated.