Hi, I have the following question:

Given that $\displaystyle x = e^{t}$, find dy/dx in terms of dy/dt and show that

$\displaystyle \frac{d^{2}y}{dx^{2}} = e^{-2t}(\frac{d^{2}y}{dt^{2}} - \frac{dy}{dt})$

So first of all, I used the chain rule to get

dy/dx = dt/dx . dy/dt

dt/dx = $\displaystyle x = e^{-t}$

so that gives me $\displaystyle \frac{dy}{dx} = e^{-t}\frac{dy}{dt}$

but how do I differentiate that a second time. I would have to be the product rule, but it's not implicit? I can't see how

Thanks