A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Given c is some constant
Why is the derivative for
d/dx Log [c x] = 1/x ?
And not
c Log [ c x]
?
anonymous
 one year ago
Given c is some constant Why is the derivative for d/dx Log [c x] = 1/x ? And not c Log [ c x] ?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I mean what kind of logical thought process should I have to lock that in ?

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4Assuming it is log based 10 \[\frac{d}{dx} \log_a(u(x)) = \frac{u'(x)}{\ln(a)*u(x)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I get that d/dx Log [x] = 1/x and normally c = 0 but then if I think chain rule .. I cook up .. Log [c x] (c)(x) (c) by constant multiple c Log[ c x ] But when I put Log [c x] into mathematica, it spits out 1/x ???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh assuming oh assuming base E

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4this formula still works for ln(x) because ln(e) = 1

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4The best way two approach derivatives is to split a function into smaller functions. For example for a function f(x) = ln(ax^2) notice f(x) is just two functions g(x) = ln(x) m(x) =ax^2 differentiate m(x) an g(x), we get g(x) = ln(x) g'(x) = 1/x m(x) =ax^2 m'(x) = 2ax now plug them into the chain rule formula f'(x) = g'(m(x))*m'(x) so pluging it in f'(x) = (1/(ax^2))(2ax)

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4the constant cancels out

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4For the derivative

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{d}{du} \ln u = \frac{1}{u} du \] if u = cx then \[ \frac{d}{dx} \ln c x = \frac{1}{cx} \frac{d}{dx} cx = \frac{c}{cx} = \frac{1}{x}\]

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4remember the derivative of ax is a

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4d/dx ax = ax^0 = a(1) = a

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4and by the chain rule formula g'(m(x))*m'(x) you should see that a wont leave the function and since it is a log it will cancel out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahh.. gotcha. *Click*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so my mistake was not taking the derivative for both sides, when applying the chain rule. Ln [ c x] u=cx Ln [u] (cx) 1/u c taking derivatives of both terms expand u back again c/cx 1/x simplified.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0probably not the best way to notate it.. but as a general identity I can say then Ln [c x] = 1/x by chain rule?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0d/dx Ln[c x] = 1/x by chain rule...

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4Look at the two graphs, note that a constant doesnt change the slope

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4or rather a constant inside a logarithm doesn't effect the slope o

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.4It just shifts the function
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.