Question

f(x)=2x+e^(2x). find derivative f-1=(4+e^4). note that f(2)=4+e^4

Answer 1

this question is poorly typed, I do not understand
f-1=(4+e^4)
please edit it so it is understandable

Answer 2

inverse function

Answer 3

you're saying the inverse function is a constant f(2) ?

Answer 4

\[f ^{-1} (4+e ^{4})\]

Answer 5

help!!! please math!!!!! due in 5 minutes

Answer 6

...cuz that's watchya wrote

Answer 7

that's the question and i don't understand it myself :/

Answer 8

wait, is it\[f^{-1}(4+e^4)\]or\[f^{-1}=(4+e^4)\]

Answer 9

Let f(x)= \[2x+e ^{2x}\]. Find d/dx (\[(f ^{-1}(4+e ^{4}))\]

Answer 10

Note that f(2)=\[4+e ^{4}\]

Answer 11

ok, hm.... sorta odd Q gotta think about it

Answer 12

oh this is easy, we just need this one formula....

Answer 13

i spent 10 mins trying to get started and couldn't even solve it. You're a super genius :)

Answer 14

and a life saver. i'm studying for my upcoming tests.

Answer 15

\[[f^{-1}](a)={1\over f'(f^{-1}(a))}\]and thanks, but I'm no genius, just someone who has practiced :)

Answer 16

whoops, typo\[[f^{-1}]'(a)={1\over f'(f^{-1}(a))}\]

Answer 17

i practice and still can't get things right :(

Answer 18

give it time ;)
anyway do you see any ways to use this formula yet?

Answer 19

yes. i can find the derivative of the f(x) function

Answer 20

well what is \(a\) in our case?

Answer 21

and yes to your above comment :)

Answer 22

a=f(2)

Answer 23

which is 4+e^4

Answer 24

excellent !
keep going

Answer 25

derivative of f(x)= 2(1+e^2x)

Answer 26

what is \[f^{-1}(a)\]?

Answer 27

2

Answer 28

so now we can just plug into the formula, right?

Answer 29

\[[f^{-1}]'(a)={1\over f'(f^{-1}(a))}\]

Answer 30

just for reminders...

Answer 31

\[1/2+2e ^{4}\]

Answer 32

that whole part after the 1 is in the denominator, right?

Answer 33

yes

Answer 34

then good job :)
congrads!

Answer 35

:) thanks! couldn't have done it without your help

Answer 36

you did most of it yourself ;)
I just posted the formula pretty much