Taking the derivative of a function

[mathgenie]

TL;DR

Derivative with respect to Gt of a function

I would like to take the derivative of the following function with respect to Gt:
$$\mathrm{G}_{t+1}=\mathrm{g}_{0}\mathrm{e}^{-qHt}$$

I think that the answer is either -1 or $\mathrm{e}^{-qHt}-1$
If you could show the calculations that would be a great help.
Thanks very much.

 

[PeroK]

TL;DR Summary: Derivative with respect to Gt of a function

I would like to take the derivative of the following function with respect to Gt:

What does this mean exactly?

 

[mathgenie]

Can you see the latex equation?

 

[PeroK]

Can you see the latex equation?

Yes.

 

[mathgenie]

I think a clue is that F(G)=Gt+1 -Gt and we want F’(G)

 

[PeroK]

I think a clue is that F(G)=Gt+1 -Gt and we want F’(G)

What about a complete statement of the problem?

 

[mathgenie]

I’ve given as much info as I can at the moment. If I was a math boff I wouldn’t be asking for help!

 

[jedishrfu]

The problem as stated isn't solvable. The righthand side has no mention of $G_t$.

and your comment that F(G)=Gt+1 -Gt = F'(G) is ambiguous.

Did you mean? $F(G) = G_{t+1} - G_t = G(t+1) - G(t)$

What is the context of the problem? Is this for a QM physics problem?

 

[mathgenie]

To reiterate, I am looking for the derivative of the difference equation $f(G)=\mathrm{G}_{t+1}-\mathrm{G}_{t}$ with respect to G.

 

[mathgenie]

It's just for my personal interest.

 

[jedishrfu]

What I meant by context is where did this equation appear? Is it from a broader physics problem?

From what you've written $G_t = G(t)$ and we are stuck because we don't know what G(t) means. You've provided a $G_{t+1}$ equation so are we to assume that

$G(t) = 0$

and $G(t+1) = g_0 e^{-qHt}$

and that $g_0$ , $H$, and $q$ are constants and that $e$ is exponential function?

 

[WWGD]

I think a clue is that F(G)=Gt+1 -Gt and we want F’(G)

Why don't you write it explicitly, $G_{t-1}=g_0e^{-qH_{t-1}}$, I assume, from the definition of $G_t$?

 

[Mark44]

I would like to take the derivative of the following function with respect to Gt:
$$\mathrm{G}_{t+1}=\mathrm{g}_{0}\mathrm{e}^{-qHt}$$

The above is not a function of $G_t$, so asking for the derivative of G with respect to $G_t$ doesn't make any sense. In the equation above, g, H, and $g_0$ appear to be constants (you haven't said what these are), and the only independent variable appears to be t. It would make sense to ask about G'(t) if you had a formula for G(t).

To reiterate, I am looking for the derivative of the difference equation $f(G)=\mathrm{G}_{t+1}-\mathrm{G}_{t}$ with respect to G.

This doesn't make any sense, either. With an explicit formula for G(t), you could find G'(t); i.e., the derivative of G with respect to t.

 

[mathgenie]

Dear all, I just wanted to thank those of you for taking a look at my post and providing suggestions. Forums like these are invaluable and although I did not get an answer to my question (no doubt due to poor phrasing of the question) I appreciate all of your time and effort in considering this question.

 

[WWGD]

@mathgenie , maybe you're considering finite element methods?

 

[Mark44]

@mathgenie , maybe you're considering finite element methods?

Or solving difference equations? The terms "first difference," "second difference," and so on are analogues to first derivative, second derivative, and so on for derivatives.