(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]x=e^t[/tex], find [tex]\frac{dy}{dx}[/tex] in terms of [tex]\frac{dy}{dt}[/tex] and hence prove [tex]\frac{d^2y}{dx^2}=e\stackrel{-2t}{}(\frac{d^2y}{dt^2}-\frac{dy}{dt})[/tex]

2. Relevant equations

3. The attempt at a solution

Well i have done the first bit:

[tex]x=e^t[/tex]

[tex]\frac{dx}{dt}=x[/tex]

[tex]\frac{dy}{dx}=x\stackrel{-1}{}\frac{dy}{dt}[/tex]

Thats fine so now to get the second derivative using product rule:

[tex]\frac{d^2y}{dx^2}=-x\stackrel{-2}{}[/tex][tex]\frac{dy}{dt}+x\stackrel{-1}{}[/tex][tex]\frac{d(\frac{dy}{dt})}{dx}[/tex]

now my problem is what is [tex]\frac{d(\frac{dy}{dt})}{dx}[/tex]?

would greatly appreciate a step by step for that part so i can finally understand this one!

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# Homework Help: Derivative of a derivative with respect to something else

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