## anonymous 3 years ago what is the derivative of ln(1+1/x)? they say the answer is xsquared-1/ xcubed+x now can someone explain how you find the answer

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1. anonymous

the answer given is correct but not simplified.... use the formula $$\large [lny]'=\frac{y'}{y}$$ to find the derivative...

2. anonymous

then how do i use this formula for the problem

3. anonymous

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 $$\large [1+\frac{1}{x}]'=$$ ????

4. anonymous

no how do u find 1+1/x? is the answer -1x-1/2

5. anonymous

use the sum rule for derivatives... $$\large [1+\frac{1}{x}]'=[1]'+[\frac{1}{x}]'$$ continue....

6. anonymous

|dw:1357167466355:dw| ??

7. anonymous

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...

8. anonymous

wait but how do i simplify to get ...|dw:1357167740926:dw|

9. anonymous

factor the top and bottom...

10. PhoenixFire

$[{x^n}]^{\prime }=nx^{n-1}$ How did you get$-x^{-{1\over 2}}$ shouldn't it be $-x^{-2}=-{1\over x^2}$

11. anonymous

oops.... sorry.... @PhoenixFire is correct...

12. anonymous

so what should i do should it look like this...|dw:1357167900420:dw|

13. anonymous

yes.. ^^^, now simplify....

14. anonymous

how....|dw:1357167986477:dw|

15. anonymous

try rewriting the denominator as...|dw:1357168045359:dw|

16. anonymous

then can i just write the answer....|dw:1357168177116:dw| or no?!?!

17. anonymous

how do i continue simplifying from what i have now?

18. anonymous

i'm double checking.... looks like this is wrong.... |dw:1357168325298:dw|

19. anonymous

well it says that is the derivative and answer and its never been wrong

20. PhoenixFire

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.

21. anonymous

the answer is wrong.... if you continue what we have, you'd get the answer produced by @PhoenixFire ...

22. anonymous
23. anonymous

just continue what we have here... |dw:1357168741789:dw|

24. anonymous

yeah i believe both of u now. okay ill just tell my teacher that it is wrong.

25. anonymous

so from the pic that u just put up

26. anonymous

yes... just continue that and you'll get the correct answer..

27. anonymous

idk exactly how to though

28. anonymous

okay i was talking about the ln not log though to start the problem... is that original answer wrong still?

29. anonymous

$$\huge \frac{\frac{-1}{x^2}}{\frac{x+1}{x}}=\frac{-1}{x^2}\cdot \frac{x}{x+1}$$

30. anonymous

|dw:1357169117534:dw|

31. anonymous

thanks for the help

32. anonymous

$$\huge \frac{\frac{-1}{x^2}}{\frac{x+1}{x}}=\frac{-1}{\cancel {x^2}x}\cdot \frac{\cancel x1}{x+1}$$

33. anonymous

@PhoenixFire , thanks for getting my back.... :) i'm a little rusty in calc... :(

34. anonymous

I like the complete lack of trying and still no understanding from this question.

35. anonymous

this was funny to watch

36. anonymous

When people don't try they don't succeed. It's that simple.

37. anonymous

still funny seeing people trying to explain to someone thats lazy

38. anonymous

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.

39. anonymous

There you go, I hope it's clear now