- #1
jaderberg
- 30
- 0
Homework Statement
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]
Homework Equations
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!