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AR15.COM
2/3/2007 4:49:28 PM EDT
what method do I need to use to differentiate x'(t) = te^(-t^2)
thats T E to the neg T squared
and if it is by parts what do I need to be using a u and dv.


Thanks in advance to anyone that helps
2/3/2007 4:52:45 PM EDT
[#1]
can't help, but thanks for the bad flashbacks.

must.go.to.happy.place.now
2/3/2007 4:58:29 PM EDT
[#2]
help
2/3/2007 5:09:50 PM EDT
[#3]

Quoted:
what method do I need to use to differentiate x'(t) = te^(-t^2)
thats T E to the neg T squared
and if it is by parts what do I need to be using a u and dv.


Thanks in advance to anyone that helps



Don't you mean integrate? ? ?
2/3/2007 5:15:31 PM EDT
[#4]

Quoted:

Quoted:
what method do I need to use to differentiate x'(t) = te^(-t^2)
thats T E to the neg T squared
and if it is by parts what do I need to be using a u and dv.


Thanks in advance to anyone that helps



Don't you mean integrate? ? ?


+1, sounds like he's asking for integration help, not differentiation help

personally i'd try a u-substitution, with u=-t^2 and du = -2t

but then again i suck at integration
2/3/2007 5:29:11 PM EDT
[#5]
If you're trying to find x(t) do it by parts using u = t and dv = exp(-t/2)

You get x(t) = u*v - integral(v*du) = -1/2 * t * exp(-t/2) + 1/2 * integral(exp(-t/2)dt)
2/3/2007 5:37:14 PM EDT
[#6]
Rewritten,

dx/dt = t * 1/[e^(t^2)]

Integrate both sides

x = S t * 1/[e^(t^2)] dt

I think that you need to do something like: Let u = t^2, du = t dt,  

But, I am weak at integration.


Dave.
2/3/2007 5:58:22 PM EDT
[#7]
Doncha love trying to communicate math with a damn k3y60^rd


PS, if you are trying to differentiate, use the product rule between t and e^-(t^2)

first times the derivative of the second plus derivative of the first times the second
2/3/2007 6:04:05 PM EDT
[#8]
I believe this is the answer, and forgive me it's been 6 years since Calc 2 in college.  With that said....

you use U substitution...

for F(t) = Se^(-t^2))  (S is the integral sign)
let u = -t^2   then du = -2tdt  and tdt = (-1/2)du  <- important

plug back in

F(t) = (-1/2)Se^udu = (-1/2)e^u

substitute back in

(-1/2)e^(-t^2))