Question

What is the derivative of: y=(1+2^x)/(1-2^x) ??

Answer 1

@satellite73

Answer 2

Quotient rule broski!

Answer 3

\[\Large\rm y'=\frac{\color{royalblue}{(1+2^x)'}(1-2^x)-(1+2^x)\color{royalblue}{(1-2^x)'}}{(1-2^x)^2}\]

Answer 4

pretty sure it's 1 over 4

Answer 5

Where you having trouble?
Differentiating the exponentail parts?

Answer 6

I already know how to use it in quotient rule and yes,.. I think exponential part is hard for me

Answer 7

Recall:\[\Large\rm \frac{d}{dx}a^x=a^x(\ln a)\]

Example:\[\Large\rm \frac{d}{dx}e^x=e^x(\ln e)\]\[\Large\rm \frac{d}{dx}e^x=e^x(1)\]\[\Large\rm \frac{d}{dx}e^x=e^x\]

Answer 8

you guys are all wrong

Answer 9

So whenever you are taking the derivative of an exponential that's NOT base e, you'll have a log showing up.

\[\Large\rm \frac{d}{dx}2^x=2^x(\ln2)\]

Answer 10

But if you want better justification than that, you can look back at logarithmic differentiation.

Answer 11

also, remember to include the point where it is not derivable

Answer 12

Hmm I think this one is differentiable over it's entire domain though, yes? :o
Or is that not what you meant? @FibonacciChick666

Answer 13

it shouldn't be at x=0, you have a vertical asympotote

Answer 14

Well that's not in the domain of the function :)
But yes, point taken.

Answer 15

true

Answer 16

but it's technically not continuous there ;P

Answer 17

you guys are all wrong

Answer 18

I'm stuck in this part: y'=((1-2^x)(2^xln2)-(1+2^x)(-2^xln2))/(1-2^x)^2

Answer 19

? why are you stuck?

Answer 20

or, what has you stuck?

Answer 21

simplifying XD

Answer 22

Ah you have to distribute and all that jazz >.<
Yah it can get a little messy.

Answer 23

oh! well, start with the easy stuff: simplify this
(1-2^x)(2^xln2)

Answer 24

how can i multiply \[(-2^xln2)*(2^x)\] ?

Answer 25

what is e^x*e^x?

Answer 26

is it the same as squared?

Answer 27

\[e^(2x)\]
yes

Answer 28

so, same here only you have 2^x*2^x

Answer 29

times your minus natural log of 2

Answer 30

no, i mean : (-2^x)*(2^x)

Answer 31

but you don't have that

Answer 32

you have \((-1)(2^x)*(2^x)\)

Answer 33

if you did, that would be as simple as it gets

Answer 34

thanks :D
that really help me

Answer 35

np