Question

what is the derivative of ln(x/2)?

Answer 1

What is \(\dfrac{d}{dx}ln(x)\)?

Answer 2

1/x

Answer 3

does it help to know that
\[\ln(\frac{x}{2})=\ln(x)-\ln(2)\]?

Answer 4

not really?

Answer 5

Okay, now remember the Chain Rule and solve your problem. Or, if you wish, the logarithm transformation can be helpful. I'd do it both ways, just to make sure it worked.

Answer 6

What's \(\dfrac{d}{dx}ln(2)\)? (The derivative of a constant?)

Answer 7

zero

Answer 8

Okay, then what is \(\dfrac{d}{dx}\left(ln(x) - ln(2)\right)\)?

Answer 9

1/x - 0

Answer 10

is that right?

Answer 11

Well, the "- 0" is a little silly.

Now do it the other way. What is \(\dfrac{d}{dx}ln\left(\dfrac{x}{2}\right)\)? Don't forget the Chain Rule.

Answer 12

1/x

Answer 13

is that right?

Answer 14

I hope so, since that what we managed the other way. How did you get that?

Answer 15

the way you showed me

Answer 16

You didn't use the Chain Rule. You used the log rules. Can you do it WITHOUT the log rules?

Answer 17

no i haven't taken calculus since high school...

Answer 18

We, then let's just go with that as it stands. Just for exposure, it looks like this:

\(\dfrac{d}{dx}ln\left(\dfrac{x}{2}\right) = \dfrac{1}{x/2}\cdot (1/2) = \dfrac{1}{x}\)

Same result. You will need the Chain Rule. Keep your eyes out for it when you trip over it again.

Good work!

Answer 19

Thanks!

Answer 20

I think the answer is wrong. Just take aut the constant and differentiate:\[\frac{ d }{ dx }\ln \frac{ x }{ 2 }=\frac{ 1 }{2 }\frac{ d }{ dx }\ln x=\frac{ 1 }{2 }\frac{ 1 }{ x }=\frac{ 1 }{ 2x }\]

Answer 21

Oh no, I just saw what i did wrong. It is 1/x.