First, simplify the original function. We need to bring the exponent down in front, split up the logarithm, and combine all the constants into one: Or, we could instead split up the logarithm first and then bring down the exponent (the order of these two operations doesn't matter): Now we have a nicely rewritten function: We've done an awful lot of work and haven't even started taking the derivative yet  but now, taking the derivative will be a piece of cake. The function f is a constant multiplied by ln x, therefore We could make this even tidier by recognizing that ln 4 = ln (2^{2}) = 2ln 2, therefore
