What Are the Proper Terms for xt and pt in Differential Equations?

[gulruozkan]

Hi,
I have question about terminology for differential equations.
Let's say that I have x, which is a function of t and p. p is also a function of t.
So x(t, p(t)) is my function.
Let's say that I take derivative of x with respect to, which will give me:
x_t + x_pp_t

In the above expression, what are x_t p_t are called? I mean terminology vise, if I want to make sensitivity analysis for the impact of t on x, t impacts x through it's own partial derivative, and through p_t .

Would I say direct effect through (x_t) vs. indirect effect through (p_t).

Would it be "first order derivative" with respect to t through x_t and "second order derivative" with respect to t through p_t?

Would it be "first level derivative" with respect to t through x_t and "second level derivative" with respect to t through p_t?

Or would it be called something entirely different?

Thanking you in advance for all your help
Gulru

 

[gtoguy97]

khIn this case, the terms that would be used are "first order derivative" and "second order derivative". The first order derivative with respect to t is xt, while the second order derivative with respect to t is pt. The terms "direct effect" and "indirect effect" could also be used to describe the impact of t on x, but these terms are not typically used in the context of differential equations.