Question

I have the answer can someone just check to see if I'm right.
WHich of the following is f '(x) for f(x)=(ln4)^x

Answer 1

So you recall that \(\large e^x\) gives us \(\large e^x\) when we differentiate it, yes?
Whenever we differentiate an exponential function that is NOT BASE e, we have to multiply by the natural log of the base.

Example:\[\large y=2^x \qquad \rightarrow \qquad y'=2^x(\ln 2)\]

We have in this problem,\[\large y=(\ln 4)^x \qquad \rightarrow \qquad y'=(\ln 4)^x(\ln(\ln4))\]It's not pretty, I know :) lol

Answer 2

ok gotit that is the answer that I had to

Answer 3

cool c: