Question

Find dy/dx

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

Answer 1

try solving

Answer 2

I attempted logarithmic differentiation but did not know how to do it with all the subtracting

Answer 3

?

Answer 4

show me your work

Answer 5

all I did was take the natural log of everything and subtracted

Answer 6

why not make it simpler by using quotient and chain rules?

Answer 7

natural log of everything?

Answer 8

because isn't the natural log easier and what would be the u in the chain rule?

Answer 9

u = -x

Answer 10

isn't it neat?

Answer 11

no I don't get it

Answer 12

set up as a quotient rule first

Answer 13

and then to the u chain rule afterwards?

Answer 14

ye

Answer 15

are you doing it or what?

Answer 16

yeah I doing it imam see how it comes out

Answer 17

the top cancels out

Answer 18

can I get some assitance

Answer 19

does it help to know that this is \(\tanh(x)\) or do you not use hyperbolic functions?

Answer 20

yeah I know what it is , is that needed

Answer 21

or you can multiply top and bottom by \(e^x\) and get
\[\frac{e^{2x}-1}{e^{2x}+1}\] if that makes it easier to use the quotient rule
there is really no way around the quotient rule here

Answer 22

okay so its just quotient rule? and messy work? could I take the natural log of everything