Question

Why is the f(x)= 4^(-x) f'(x)= -4^(-x)ln4. I understand the rule b^x = b^xlnb, just confused where the - attached to the 4 came from

Answer 1

You're taking the derivate of b^(-x), not b^x, so you have to use the chain rule aswell:
\(\Large f(x) = 4^{-x}\)
\(f'(x) = 4^{-x}\ln 4 * [-x]' = -4^{-x} \ln 4\)