Question

calculus help! can some check my answer to the following q? find the derivative of the function.......y=(1+e^x/1-e^x)

Answer 1

i mean y=ln(1+e^x/1-e^x)

Answer 2

i got y(prime)=1/x

Answer 3

Seperate the logarithm using the log properties

so y= ln(1+e^x) - ln(1-e^x)

the derivative of ln(x) = 1/(u) *u'

Answer 4

derivative of ln(u) = 1/(u) * u'

Answer 5

u lost me

Answer 6

dido got it

Answer 7

Okay I will solve it...

Answer 8

well i dont and i am the one w. the question

Answer 9

\[\frac{d}{dx}\ln(f(x))=\frac{f'(x)}{f(x)}\]

Answer 10

NO! i NEED to NOW this STUFF!

Answer 11

know it now

Answer 12

i mean KNOW!

Answer 13

i now you meant that
you got it? take the derivative of the inside piece, divide it by the inside piece. that is all

Answer 14

y' = (1/(1+e^x)) *e^x +(1/(1-e^x))* (-e^x))
y' = (e^x)/(1+e^x) + (-e^x)/(1-e^x)

Answer 15

you can just about do it in your head with a little practice

Answer 16

I won't bother simplifying that.

Answer 17

thanks 4 making fun of me satellite 73 :p

Answer 18

you know i am only funnin

Answer 19

Funning haha...

Answer 20

you got this or no?

Answer 21

lololohaha but no seriously i dont understand it:{

Answer 22

ok lets do this one
\[\ln(\sin(x))\] in your head you can write \[\frac{\cos(x)}{\sin(x)}\]

Answer 23

the derivative of sine is cosine, that goes up top, sine goes in the bottom

Answer 24

\[\ln(x^2+2x)\] derivative is
\[\frac{2x+2}{x^2+2x}\] just like that

Answer 25

derivative of inside piece up top, inside piece itself down below

Answer 26

okay but no......wait! ur confusing the beJesus outta me :IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Answer 27

ok i will shut up and wait

Answer 28

no dont shut up........shut up while taking it too fats maybe going slower? explaining each step?

Answer 29

fast i mean UGH!

Answer 30

you are asked for the derivative of the log of something right? i mean something other than just \(x\)

Answer 31

ok?

Answer 32

so i will say you are asked for the derivative of \(\ln(f(x))\) i.e. the log of some other function of \(x\)

Answer 33

so far so good?

Answer 34

ehhhhhhhhhhhh i guess :I

Answer 35

like for example
\(\ln(1+e^x)\)

or \(\ln(\sin(x)\)

or \(\ln(x^2+2x)\)

Answer 36

in other words the log of something

\(\ln(\text{something})\)

Answer 37

we good so far?

Answer 38

yes

Answer 39

check your work on: wolframalpha.com

Answer 40

ok so this is how you do it:
make a fraction
take the derivative of the inside piece, put it up top
put the inside piece itself in the denominator

Answer 41

okay

Answer 42

that is all

Answer 43

so how about
\[\ln(\sin(x))\]?

Answer 44

its ln(cosx/sinx)

Answer 45

it would be without the log

Answer 46

o.

Answer 47

y?

Answer 48

i can explain if you like, lets get a correct answer first

Answer 49

k

Answer 50

so?

Answer 51

um. do i do the sma e4 my prob right??

Answer 52

yes

Answer 53

same

Answer 54

for my problem?

Answer 55

yes

Answer 56

after you simplify as suggested
that is after you write
\[\ln(1+e^x)-\ln(1-e^x)\]

Answer 57

will i have e^x/1+e^x?

Answer 58

for the first term, yes

Answer 59

okay and i am supposed 2 do this as well to the second term?

Answer 60

yes

Answer 61

satellite 73?

Answer 62

o okay and then do i do the quotient rule for both or wat?

Answer 63

no then you are done

Answer 64

what?! really?!

Answer 65

you don't take the derivative twice! not unless you want the second derivative

Answer 66

i think you are confused as to what we are doing
we are not simplifying the expression, we are finding the derivative

Answer 67

o okay thanks i think that is all for today thanks for helping me i really appreciate it...i dont have my brother to help me since he went back to school and its been pretty tough having that i am sucky at math THANK YOU!

Answer 68

yw, hope it is clear, and also hope it is clear that it is easy to do!
derivative of \(\ln(\sin(x))\) is \(\frac{\cos(x)}{\sin(x)}\)
derivative of \(\ln(x^2+2x)\) is \(\frac{2x+2}{x^2+2x}\)
derivative of \(\ln(1+e^x)\) is \(\frac{e^x}{1+e^x}\)

Answer 69

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Answer 70

lol