Question

How do you find dx/dy given that y(x)=e^x - e^-x . I know that dx/dy = 1/(dy/dx) but I'm not sure how to proceed.

Answer 1

\[f(x)=e^x-e^{-x}\] take the derivative, knowing two facts: the derivative of \(e^x\) is itself, and the derivative of \(e^{-x}\) is \(-e^{-x}\) by the chain rule or quotient rule whichever you prefer

Answer 2

But that's not all though. Notice that you need to find "dx/dy" instead of "dy/dx".

Answer 3

I'm thinking that you need to differentiate implicitly:- \[1 = \frac{ dx }{ dy } e ^{x}+\frac{ dx }{ dy } e ^{-x}\]

Answer 4

But now, you need to convert the x's into y.

Answer 5

before that, the equation will become:- \[\frac{ dx }{ dy }=\frac{ 1 }{ e ^{x}+e ^{-x} }\]

Answer 6

Since it is in terms of y, I need to turn all x's into y's. This is where I'm stuck at.