Question

how do you find the log of a square root?

Answer 1

log sqrt(x) = log x^(1/2) = (1/2)logx

Answer 2

ok, I have the log of the square root of x^2 +2 ?????

Answer 3

ok, then log sqrt(x^2 + 2) = log (x^2 + 2)^(1/2) = (1/2)log (x^2 + 2)

Answer 4

do you know how to find the derivative of it?

Answer 5

yes, use the following, d/dx(logu) = 1/ulna

Answer 6

let u = x^2 + 2, then y = logu^(1/2) = (1/2)logu = (1/2)/ulna = (1/2)/(x^2 + 2)lna

Answer 7

u did not specify base a however

Answer 8

its the application of the chain rule to the derivative of a logarithm with base a , provided a > 0

Answer 9

i do not even know what you mean by that. the whole problem is to differentaite x^5 divided by (1-10x)(sqrt ofx^2 +2)

Answer 10

ok so u want me to differentiate x^5/(1-10x)(sqrt(x^2 + 2))?

Answer 11

srry, i thought u wanted me to to differentiate log sqrt(x^2 + 2) my bad

Answer 12

yes but I need to know specifically how to do the expression involving the square root. I cannot understand that; maybe it's the algebra involved to figure it out? /can you do the whole problem, focusing on how you get the derivative of the square root?

Answer 13

sure :)

Answer 14

ur my last client for this morning, i gotta go shower after this

Answer 15

well I sure am glad I found you! Thanks!

Answer 16

ok since, this is an ugly problem for application of the quotient rule, we r going to let y equal the expression and take the natural log of both sides

Answer 17

go on, pls

Answer 18

are you still there?

Answer 19

whats the question?

Answer 20

I need to find the derivative of x^5/(1-10X)(sqrtx^2+2) using logs.

Answer 21

My problem is the expression with the sqrt in it. the others I am comfortable with finding, but that sqrt is killing me!

Answer 22

\[\frac{x^5}{1-10x}*\sqrt{x^2 +2}\] is this the equation? or is that sqrt stuck under the bar?

Answer 23

the square root is stuck under the bar next to the (1-10x)

Answer 24

got it..... and why do we have to use logs to do this? is that in the directions? or something you thought might help?

Answer 25

it was in the instructions to do so.

Answer 26

odd instructions :)

Answer 27

are they? I am so new to this, 2 weeks into calc and I think the objective was teach us logs and how to differentiate them using all the forms of expressions possible.

Answer 28

\[\frac{\log(x^5)}{\log[(1-10x)(\sqrt{x^2+2})]}\]

Answer 29

yes!

Answer 30

anything with an exponent gets dragged to the fron....like this:

5 log(x) ..... that takes care of the top right? or at least is a step we can take..now for th e bottom

Answer 31

log(ab) = log(a) + log(b)

sooooo.....

log(1-10x) + log[sqrt(x^2 +2)] right so far?

Answer 32

yes

Answer 33

do you recall that radicals such as squaree roots and cube roots and the like are fraction exponentes?

sqrt(4) = 4^(1/2) = 2 right?

Answer 34

yes

Answer 35

good; and after all that work i see a mistale that my brain made lol.... we first need to take the log of the whole entire fraction; not portions of it :)

Answer 36

then we can split it up lol

Answer 37

\[\log(\frac{a}{b*c}) = \log(a)-[\log(b)+\log(c)]\] like this :)

Answer 38

I trust you! go on! brain mistakes are allowed! ; )

Answer 39

\[5 \log(x) - [\log(1-10x) + \frac{1}{2}\log(x^2+2)]\]

Answer 40

\[5 \log(x) - \log(1-10x) - (1/2)\log(x^2+2)\]

Answer 41

thats as basic as you can get it; now take the derivatives :) and the "log" part doesnt have to be "log" it can also be "ln"; the natural log...ln migh tmake life easier with derivatives

Answer 42

\[Dx[5 \ln(x) - \ln(1-10x) - \frac{1}{2}\ln(x^2+2)]\]

Answer 43

5/x
- 1/(1-10x)
- 1/(x^2+2)

Answer 44

the derivative of ln(x) = Dx/x

Answer 45

that second term should be: -10/(1+10x) then :)

Answer 46

.....ack!!!

+10/(1-10x) ill get it right eventually lol

Answer 47

youre great! Pls don't apologize!

Answer 48

did it make sense what I did :)

Answer 49

so far it makes sinse except where you said that it was a +10. I thought the whole equation was the expression -another expression-another expression. Why the +?

Answer 50

the middle term in logs is :

- ln(1-10x)

the derivative of ln(....) is:

the derivative of (....) derivative of (1-10x)
------------------ = ------------------
(....) (1-10x)
the second term the becomes.... dont forget the initial (-) in fron of it



-10x
- ------ = +10/(1-10x) :)
(1-10x)

Answer 51

ok it's the "negative minus a negative gives a positive" thing, right?

Answer 52

exactly :)

Answer 53

ok, let's move to the sqrt thing...I cannot stand the suspense!

Answer 54

2 negative always gives a positive;

-5(-3) = 15

7--3 = 10

-6/-3 = 2

-6 -2 = -8....except for that one lol

Answer 55

; )

Answer 56

the sqrt became the thrid term:

- 1/2 ln(x^2+2) right? which derives to...

1 2x
- -- ------- = -x/(x^2+2) right?
2 (x^2+2)

Answer 57

no how did you get that?

Answer 58

tell me the last part that makes sense to you and i can unravel the mystery from there :)

Answer 59

i understand where you got the third term -1/2 ln(x^2+2), but finding the derivative of it is where I am baffled.

Answer 60

i had to switch to firefox, IE acts wierd on this site

Answer 61

ok....

Do we have to derive the -1/2 part? or can we pull it aside and leave it alone?... visually that is.

Answer 62

D(5a^2) = 5 D(a^2) = 5 (2a) = 10a right?

Answer 63

leave it alone visually is fine. I understand that it has to be put back in when we are done.

Answer 64

good;

then lets derive the ln(x^2+2) part :)

D(x^2 +2)
--------- right? so all we really have to do is derive the top
(x^2 +2)

Answer 65

OMG! I get it!!!!!!!!!!!!!!!!! Can I try to explain it you so I know for sure?

Answer 66

you can try :)

Answer 67

Ok, give me a minute to write it all down then type it to you, but I am going to work only with the sqrt expression since that was the one giving me trouble. Can you hold for like 2 minutes?

Answer 68

illl be around :)

Answer 69

ok, here goes. i will do my best with the ^ sign and stuff, ok? Are yo with me? Here goes:::::: d/dx(ln(x^2+2)^1/2) = -1/2(ln(x^2+2)) = -1/2(1/x^2+2)d/dx(x^2+2) = -1/2(1/x^2+2)(2x) = -2x/2(x^2+2) = (after canceling out the 2) -x/(x^2+2) Am I right? Is that the derivative of the natural log of the sqrt of x^2+2?

Answer 70

that is very good :) except for the spurious (-) sign which is just a result of it being the third term subtracted from the others... it looks like you got a handle on it :)

Answer 71

should the 1/2 be then positive or negative?

Answer 72

it should be positive since if it were standing all alone by itself:

Dx[ln(x^2+2)^(1/2))] = Dx[(1/2) ln(x^2+2)] =

1/2 Dx(ln(x^2+2))

1/2 2x/x^2+2

the 2s cancel to give you...

x/(x^2 + 2) :)

Answer 73

thank you, thank you, thank you!!! You helped me when no one else could make me understand! Can I give yuou a medal for this?

Answer 74

you can if you want ;)

Answer 75

how do I do that exactly?

Answer 76

you night have to press your refresh button on your browser...its usually just the f5 button on te keyboard.

That will refresh the page and allow you to see a "give medal" option next to my name :)

Answer 77

ok, IO will do that now, although I agree that IE is weird with this; the page kept scrolling up and down on its own! i like Firefox so much better, but MathXL only works with IE.

Answer 78

is MathXL a program you are working with?

Answer 79

did the refresh work out for you?