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#1 2006-03-22 21:29:34

JamesMichael
Guest

Differentiation Question?

Hello guyzz...

I was wondering how those functions can be differentiated with respect to t. I found it a bit challenging. Can anyone found the derivative of those functions?

1. f(t) = exp(μt +  (σ^2)(t^2)/2).  ( exp is just e and the things in the bracket are the power of the e)

2. f(t) = (1 - βt)^α        t< 1/β

3. f(t) = e^u((e^t) - 1)

James

#2 2006-03-22 22:01:53

gnitsuk
Member
Registered: 2006-02-09
Posts: 119

Re: Differentiation Question?

TWO

y = (1 - bt)^a

Take logs to base e of both sides =>

ln(y) = a*ln(1 - bt)

Differentiate both side wrt t =>

(1/y)(dy/dt) = a*(-b/(1 - bt)) =>

dy/dt = a*(-b/(1 - bt))*(1 - bt)^a = -ab(1-bt)^(a - 1)

ONE

y = e^(ut + s^2t^2/2)

This is a function of a function - has form y = e^(f(t)) so differential is dy/dx = f'(t)*e^(f(t)) - so we have:

dy/dt = (u + s^2t)e^(ut + s^2t^2/2)

THREE

y = e^(u(e^t - 1)) - same thing again -

dy/dt  = (u*e^t - 1)e^(u(e^t - 1))

Last edited by gnitsuk (2006-03-22 22:05:26)

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#3 2006-03-22 23:05:44

JamesMichael
Guest

Re: Differentiation Question?

woow..
it seems that differentiating those functions was like a piece of cake for you.
I think those functions can also be differentiated in some different way.

Anyways..thanks a lot..

I will post some integration questions and hope that you can evaluate those integrals

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