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anonymous
 5 years ago
Hey guys I'm having problems with derivatives if someone could explain the logx/lnx derivatives to me that would be great heres a few examples y = 2x^2(lnx)^4 or y = ln((x +1)/x)
anonymous
 5 years ago
Hey guys I'm having problems with derivatives if someone could explain the logx/lnx derivatives to me that would be great heres a few examples y = 2x^2(lnx)^4 or y = ln((x +1)/x)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0to start, do you know the derivative of \[\ln(x)\] ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[d/dx [ \ln (x) ] = 1/x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes i just dont understand how it applies when you have things attached to x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0such as the (lnx)^4 or the ln(x +1/x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let's try \[\ln((x+1)/x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0have you used substitution rule before?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That example is very simple, though the process might be tedious. Simply put a 1 over the expression then multiply by derivative of the expression

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, i got that wrong, i was describing log.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm contradicting myself, I think i told you right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0using the substitution rule: let's have \[u = (x+1)/x , du = 1/x^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok sorry the substitution thing is confusing me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, well, the concept is thus: essentially you can simply things by taking a difficult expression to immeditaely differentitate, like here ln((x+1)/x), and simplify the first steps a bit

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0outright, [ln((x+1)/x)]' looks difficult, but [ln(u)]'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that is like a calc identity

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the trick is keeping track of this substitution, you'll need to find the derivtative of u. as above, u=(x+1)/x, while du = (1/x^2)*dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ahhh ok so if you set it as a variable it complicates things less

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we have our first equation: ln((x+1)/x) dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, you do less internal variable manipulation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yep that helped a lottt

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, you want to solve it? i can stay to help if you need it...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but just to be sure once I have the x + 1 over x I have to then use quotient rule...?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, u = (x+1)/x ... but that equals x/x + 1/x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, whats the derivative with respect to x of 1 + x^1 ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, ln(u) du > but du = (1/x^2)*dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ln(u)' > 1/u, where u is (1 + 1/x) ....so you have \[1/[(1 + 1/x)]\]....then, you can't forget that du was 1/x^2 * dx, so when you now substitute back in for u so you have the original variable x, you have to multiply by (1/x^2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{1}{(1+1/x)} * \frac{1}{(x^2)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which you can simplify

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok sorry my computers really crappy so i cant reply fast but i completely get it now thanks!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no problem, hopefully now you can use the book examples much better too!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0also, here on OpenStudy, if someone gives you good help, you can award them with a medal here in the conversation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, ask more questions and maybe you can help some other math learners if you see a question you know to answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i'm off, but good luck with the calc ;)
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