A simple derivative that I can't get for the life of me

[trap101]

Trying to get the 2nd derivative of this expression:

ps/(1-qs) where p,q are constants and s is the variable. The solution is 2pq²(1-qs)³


for the life of me I can't get that solution. every time I do it I get 2q/(1-q)²

maybe I should mention that I'm using a probability generating function and trying to get the 2nd moment for the geometric distribution. But that shouldn't have an effect on the simple fact of the 2nd derivative.

 

[jhae2.718]

Make sure you use the product or quotient rule and apply the chain rule properly.

 

[trap101]

I've been doing that.

 

[Dick]

I've been doing that.

Shouldn't your answer at least depend on s? That said, I don't get the answer you show as a solution either.

 

[ehild]

How did you loose the "s" from the denominator? Show your work in detail.

ehild

 

[Levi Tate]

I didn't get that answer either that you show as a solution.

I got qp+q^2ps/(1-qs)^3

 

[phiiota]

whenever i have a problem like this, i like to move my constants out front and rewrite things in fractions as negative exponents. in your case, i would rewrite the function as

ps/(1-qs)=p*(s)(1-qs)^-1. then, ignore the p for now, since you can just multiply it out, and focus on find the derivative of s*(1-qs)^-1. should be pretty easy from there out. if i want to be more explicit, i write things out in function notation first, apply the chain rule/product rule (as i would here) with f(s),g(s), etc, and then plug in f(s),f'(s), etc, after I've figured out the proper form.

 

[skiller]

I didn't get that answer either that you show as a solution.

I got qp+q^2ps/(1-qs)^3

...which is also incorrect.

 

[Levi Tate]

Is it, I did the problem while sleeping, why don't you post a solution oay?

 

[skiller]

Is it, I did the problem while sleeping, why don't you post a solution oay?

I could post the solution, but it's not the done thing. People asking the questions should show their work so far. The OP hasn't yet.

 

[trap101]

the reason the "s" disappears from the solution is because it is a PGF from statistics so after you differentiate you let s = 1 and obtain your solution.

 

[Dick]

the reason the "s" disappears from the solution is because it is a PGF from statistics so after you differentiate you let s = 1 and obtain your solution.

"But that shouldn't have an effect on the simple fact of the 2nd derivative." You said you were just trying to find the second derivative. So why is there an s in the given solution?

 

[skiller]

the reason the "s" disappears from the solution is because it is a PGF from statistics so after you differentiate you let s = 1 and obtain your solution.

Ok, so you haven't asked for the 2nd derivative at all, then. Make your mind up.

 

[skiller]

I didn't get that answer either that you show as a solution.

I got qp+q^2ps/(1-qs)^3

Are you suggesting yours is correct?

 

[Levi Tate]

No buddy i said i was falling asleep, so i am going to do the problem again now and i don't know if this boy here is talking about statistics and i don't know if i am right, i never know if i am right, but this here is what i get,

D^2y/(dx)^2= 8pq^3/(1-qs)^5

oh i took the second derivative of the second derivative that was given in the problem.

So it would be the 4th derivative of the solution given in the initial problem, which was said to be wrong for that problem, so this is just the second derivative of that proposed solution then, eh.

 

[skiller]

No buddy i said i was falling asleep, so i am going to do the problem again now and i don't know if this boy here is talking about statistics and i don't know if i am right, i never know if i am right, but this here is what i get,

D^2y/(dx)^2= 8pq^3/(1-qs)^5

oh i took the second derivative of the second derivative that was given in the problem.

So it would be the 4th derivative of the solution given in the initial problem, which was said to be wrong for that problem, so this is just the second derivative of that proposed solution then, eh.

Fine. No problem, try again tomorrow.

 

[Ray Vickson]

Trying to get the 2nd derivative of this expression:

ps/(1-qs) where p,q are constants and s is the variable. The solution is 2pq²(1-qs)³


for the life of me I can't get that solution. every time I do it I get 2q/(1-q)²

maybe I should mention that I'm using a probability generating function and trying to get the 2nd moment for the geometric distribution. But that shouldn't have an effect on the simple fact of the 2nd derivative.

You say "I can't get that solution". I should hope not: the correct solution is
2pq/(1-qs)^3. Can you get that?

RGV