# Thread: Natural log derivatives? How?

1. ## Natural log derivatives? How?

This is the equation I have:

Let $f(x) = -4 \ln(5 x)$
Find $f'(x) =$

My Work Sheet says the answer is:
$
-4/x
$

My question is, shouldn't it be somthing like:
$
-20/5x
$

...when you derive $ln(5 x)$ shouldn't it become $1/5x$ and from there don't you have to use the chain rule on $5x$ and get 5?

It seems to me you would only get $-4/x$ if $f(x) = -4 \ln(x)$

What is it I don't understand?! Thank You

2. the thing with natural log derivatives is that (d/dx) ln(x) is actually (1/x)*x' (so 1 divided by the inside, then times the derivative of the inside)

-4ln(5x) becomes -4*(1/5x)*5 = -4/x

3. Wow -20/5x = -4/x...

Im dumb... haha I guess that's what doing hours upon hours of math does... just scrambles the brain.