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.

Question

anonymous · Answer

$$f(x)=e^x-e^{-x}$$ 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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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