The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Differential of ln

I know if you have ln[f(x] you differentiate it by using:

f'(x)/f(x)

but what if you have

I tried to use the above rule but I am not getting the correct answer. Am I using the correct method?
Reply 1
Avatar for Ateo
Ateo
9
Original post by GPODT
I know if you have ln[f(x] you differentiate it by using:

f'(x)/f(x)

but what if you have

I tried to use the above rule but I am not getting the correct answer. Am I using the correct method?


Change of base rule.
I like to move it move it, she like to move it move it, we like to MOVE IT!
Use chain rule. Let u = the bit inside your log. Then do dy/dx = du/dx * dy/du
Reply 4
Avatar for GPODT
GPODT
OP
16
Original post by Ateo
Change of base rule.

I have used this before but can you elaborate because I am slightly confused..
Reply 5
Avatar for joostan
joostan
13
Original post by GPODT
I have used this before but can you elaborate because I am slightly confused..


logax = ln(x)/ln(a)
Reply 6
Avatar for GPODT
GPODT
OP
16
Original post by joostan
logax = ln(x)/ln(a)

What base do we change it to?
Reply 7
Avatar for joostan
joostan
13
Original post by GPODT
What base do we change it to?

You want to convert to ln, so that you can apply rules of calculus. Above is the specific change of base formula to do so :smile:
Reply 8
Avatar for davros
davros
16
Original post by GPODT
I know if you have ln[f(x] you differentiate it by using:

f'(x)/f(x)

but what if you have

I tried to use the above rule but I am not getting the correct answer. Am I using the correct method?


Is your log the natural log (ln) or log to another base?

Regardless, you still use the chain rule for this problem.
Reply 9
Avatar for GPODT
GPODT
OP
16
Original post by joostan
You want to convert to ln, so that you can apply rules of calculus. Above is the specific change of base formula to do so :smile:


Original post by davros
Is your log the natural log (ln) or log to another base?

Regardless, you still use the chain rule for this problem.


Yes this is the natural log. Apologies for the confusion, Wolfram Alpha interpreted ln as log..

I used the chain rule (probably incorrectly). So I differentiated x+(1+x2)0.5 and divided this differential by x+(1+x2)0.5
Reply 10
Avatar for joostan
joostan
13
Original post by GPODT
Yes this is the natural log. Apologies for the confusion, Wolfram Alpha interpreted ln as log..

I used the chain rule (probably incorrectly). So I differentiated x+(1+x2)0.5 and divided this differential by x+(1+x2)0.5


This should give you the correct answer.
Also the equation you have been given is equivalent to arcsinh(x)
Your formula book should have the derivative of arcsinh(x) for you to check with.
(edited 11 years ago)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you