Question

A function is given by f(x) ln(e^x + e^-x +2)

Find a) f ' (x)
and b) f '' (x)

Thank you ppl.

Answer 1

d/dx ( lnf(x) ) = f'(x) /f(x)

Answer 2

e^x -e^-x / e^x+e^-x +2

Answer 3

lalaly, I have 8 options to choose from and that is not an option for f'(x)

Answer 4

nw use the quotient rule for f''(x)

(e^x -e^-x)(e^x+e^-x+2) -(e^x-e^-x)(e^x-e^-x) / (e^-x+e^x+2)^2

Answer 5

wht are the options

Answer 6

my answer can be simplifed to e^x - 1 / e^x +1

Answer 7

lol both f'(x) and f''(x) should come from these:

1 / (e^x - e^-x)

2/e^x + e^-x + 2

e^x + e^x / e^x + e^-x + 2

e^ - e^-x / e^x + e^ -x + 2

2(e^2x + e^-2x) / (e^x + e^-x + 2)^2

2(e^x + e^-x)/(e^ + e^-x + 2)^2

- (e^x + e^-x) / (e^x - e^-x)^2

e^x - e^-x / e^2x + e^-2x

Answer 8

what lalaly posted the first time is there, its the 4th one from the top.

Answer 9

thanx joe :D ...

Answer 10

Ooops sorry lalay, I missed it :(

what about f ''(x) ?

Answer 11

is that the fifth on on the list?

Answer 12

wait i did not simplify it

Answer 13

i think you get
\[f'(x)=\frac{e^x-1}{e^x+1}\] is that an option?

Answer 14

maybe easiest to use the quotient rule for f' in this form

Answer 15

sorry satelite it's not ... lalaly has helped me with f ' (x) ... it's the fourth one on my list above.

Answer 16

oh so i see. i should read more carefully. strange though...

Answer 17

I still her solution for f '' (x) simplified though so i can see if that is the fifth or sixth on the list.