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Alkmene
Topic Author
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Neftci exercise question

Can anyone explain the solution to the first exercise in chapter 18; step 3 to step 4: not clear on why exp(at)*(drt + artdt) = del(exp(at)*rt/deltwhere in rt the t is a subscript on r.Thanks for any insights.
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Mathematics - Neftci1.zip

stilyo
Posts: 166
Joined: January 12th, 2009, 6:31 pm

### Neftci exercise question

product rule - d/dt[f(t)g(t)]=df(t)/dt*g(t)+f(t)*dg(t)/dt, isn't that it?

Alkmene
Topic Author
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Neftci exercise question

Stilyo,thanks for your reply.I am sure the product rule is relevant but I still can't see the result:f(t) = exp(at)g(t)=rt (here I am not sure how to deal with t being the subscript)d f(t)/dt = aexp(at)dg(t)/dt = ?for the solution to be as suggested exp(at)*(drt + artdt),d rt/dt would have to be (drt+artdt-art).why is this so?thanks a lot for your help.Alk

stilyo
Posts: 166
Joined: January 12th, 2009, 6:31 pm

### Neftci exercise question

f(t)=exp(at)g(t)=r(t)=>in differential form, the product rule is d(f(t)*g(t))=df(t)*g(t)+f(t)*dg(t)df(t)=a*exp(at)dtdg(t)=dr(t)=> d(exp(at)*r(t))=(a*exp(at)dt)*r(t)+exp(at)*dr(t)=exp(at)*(a*r(t)dt+dr(t))

Alkmene
Topic Author
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Neftci exercise question

sorry, that was a bit rushed and the notation should read "del" for all the derivatives as these are only partial derivatives and NOT with regards to the random part of the fucntion; at least this is how I read the suggested solution.Thanks again for any clarification.Alk *edit*: but then again, the dWt is also a function of time. Confused how to approach this. Thanks.
Last edited by Alkmene on September 20th, 2010, 10:00 pm, edited 1 time in total.

Alkmene
Topic Author
Posts: 301
Joined: January 18th, 2007, 10:19 pm

### Neftci exercise question

QuoteOriginally posted by: stilyof(t)=exp(at)g(t)=r(t)=>in differential form, the product rule is d(f(t)*g(t))=df(t)*g(t)+f(t)*dg(t)df(t)=a*exp(at)dtdg(t)=dr(t)=> d(exp(at)*r(t))=(a*exp(at)dt)*r(t)+exp(at)*dr(t)=exp(at)*(a*r(t)dt+dr(t))Merci!