Question

What is the derivative of f(x) = ln(e^2x)?

Answer 1

if you know the rules of logarithms you can see that this can be reduced to:
\[f(x)=2xln(e)=\ln(e ^{2x})\]
and the you should also know that the natural log is the compositional inverse function of the e^x. this means that ln(e) = 1

Answer 2

I understood the first step where you pulled the exponent down in front, but I'm not sure about the next part.

Answer 3

since the log and the exponential are inverses, that means \[\ln(e^{\text{whatever}})=\text{whatever}\]

Answer 4

so you are in fact just looking at \[f(x)=2x\] and the derivative is real easy

Answer 5

so the ln cancels out the e and simply 2x is left?