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 2 years ago
what is the derivative of ln(1+1/x)?
they say the answer is xsquared1/ xcubed+x
now can someone explain how you find the answer
 2 years ago
what is the derivative of ln(1+1/x)? they say the answer is xsquared1/ xcubed+x now can someone explain how you find the answer

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dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1the answer given is correct but not simplified.... use the formula \(\large [lny]'=\frac{y'}{y} \) to find the derivative...

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0then how do i use this formula for the problem

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1let \(\large y=1+\frac{1}{x} \) so, \(\large [ln(1+\frac{1}{x})]'=\frac{[1+\frac{1}{x}]'}{1+\frac{1}{x}} \) can you find \(\large [1+\frac{1}{x}]'= \) ????

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0no how do u find 1+1/x? is the answer 1x1/2

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1use the sum rule for derivatives... \(\large [1+\frac{1}{x}]'=[1]'+[\frac{1}{x}]' \) continue....

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1357167466355:dw ??

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1ok... good... so, \(\large [ln(1+\frac{1}{x})]'=\frac{[1+\frac{1}{x}]'}{1+\frac{1}{x}}=\frac{x^{(\frac{1}{2})}}{1+\frac{1}{x}} \) now just simplify...

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0wait but how do i simplify to get ...dw:1357167740926:dw

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1factor the top and bottom...

PhoenixFire
 2 years ago
Best ResponseYou've already chosen the best response.1\[[{x^n}]^{\prime }=nx^{n1}\] How did you get\[x^{{1\over 2}}\] shouldn't it be \[x^{2}={1\over x^2}\]

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1oops.... sorry.... @PhoenixFire is correct...

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0so what should i do should it look like this...dw:1357167900420:dw

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1yes.. ^^^, now simplify....

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0how....dw:1357167986477:dw

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1try rewriting the denominator as...dw:1357168045359:dw

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0then can i just write the answer....dw:1357168177116:dw or no?!?!

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0how do i continue simplifying from what i have now?

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1i'm double checking.... looks like this is wrong.... dw:1357168325298:dw

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0well it says that is the derivative and answer and its never been wrong

PhoenixFire
 2 years ago
Best ResponseYou've already chosen the best response.1Every time I do it I get \(\large {1 \over x^2+x}\) I think the answer that it's given you is wrong. Unless you are accidentally looking at the wrong question in the answer section. I do that all the time.

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1the answer is wrong.... if you continue what we have, you'd get the answer produced by @PhoenixFire ...

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1and wolfram... http://www.wolframalpha.com/input/?i=derivative+ln%281%2B1%2Fx%29

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1just continue what we have here... dw:1357168741789:dw

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i believe both of u now. okay ill just tell my teacher that it is wrong.

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0so from the pic that u just put up

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1yes... just continue that and you'll get the correct answer..

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0idk exactly how to though

kobe24
 2 years ago
Best ResponseYou've already chosen the best response.0okay i was talking about the ln not log though to start the problem... is that original answer wrong still?

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1\(\huge \frac{\frac{1}{x^2}}{\frac{x+1}{x}}=\frac{1}{x^2}\cdot \frac{x}{x+1} \)

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1\(\huge \frac{\frac{1}{x^2}}{\frac{x+1}{x}}=\frac{1}{\cancel {x^2}x}\cdot \frac{\cancel x1}{x+1} \)

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1@PhoenixFire , thanks for getting my back.... :) i'm a little rusty in calc... :(

malevolence19
 2 years ago
Best ResponseYou've already chosen the best response.0I like the complete lack of trying and still no understanding from this question.

malevolence19
 2 years ago
Best ResponseYou've already chosen the best response.0When people don't try they don't succeed. It's that simple.

Rowa
 2 years ago
Best ResponseYou've already chosen the best response.0still funny seeing people trying to explain to someone thats lazy

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.0I don't know if your teacher want's you to simplify that, that's not the kind of "simplifying exercise" it looks like it's just to learn the Ln derivative, I took a picture, sorry i'm very traditional, hope it helps you.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.0There you go, I hope it's clear now
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