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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
 one year ago
 one year 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
 one year ago
 one year ago

This Question is Open

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

kobe24Best ResponseYou've already chosen the best response.0
then how do i use this formula for the problem
 one year ago

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

kobe24Best ResponseYou've already chosen the best response.0
no how do u find 1+1/x? is the answer 1x1/2
 one year ago

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

kobe24Best ResponseYou've already chosen the best response.0
dw:1357167466355:dw ??
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
ok... 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...
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
wait but how do i simplify to get ...dw:1357167740926:dw
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
factor the top and bottom...
 one year ago

PhoenixFireBest 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 \[x^{2}={1\over x^2}\]
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
oops.... sorry.... @PhoenixFire is correct...
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
so what should i do should it look like this...dw:1357167900420:dw
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
yes.. ^^^, now simplify....
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
how....dw:1357167986477:dw
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
try rewriting the denominator as...dw:1357168045359:dw
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
then can i just write the answer....dw:1357168177116:dw or no?!?!
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
how do i continue simplifying from what i have now?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
i'm double checking.... looks like this is wrong.... dw:1357168325298:dw
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
well it says that is the derivative and answer and its never been wrong
 one year ago

PhoenixFireBest ResponseYou've already chosen the best response.1
Every 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.
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
the answer is wrong.... if you continue what we have, you'd get the answer produced by @PhoenixFire ...
 one year ago

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

dpaIncBest ResponseYou've already chosen the best response.1
just continue what we have here... dw:1357168741789:dw
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
yeah i believe both of u now. okay ill just tell my teacher that it is wrong.
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
so from the pic that u just put up
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
yes... just continue that and you'll get the correct answer..
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
idk exactly how to though
 one year ago

kobe24Best ResponseYou've already chosen the best response.0
okay i was talking about the ln not log though to start the problem... is that original answer wrong still?
 one year ago

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

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

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

malevolence19Best ResponseYou've already chosen the best response.0
I like the complete lack of trying and still no understanding from this question.
 one year ago

malevolence19Best ResponseYou've already chosen the best response.0
When people don't try they don't succeed. It's that simple.
 one year ago

RowaBest ResponseYou've already chosen the best response.0
still funny seeing people trying to explain to someone thats lazy
 one year ago

GCR92Best ResponseYou've already chosen the best response.0
I 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.
 one year ago

GCR92Best ResponseYou've already chosen the best response.0
There you go, I hope it's clear now
 one year ago
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