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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_{p}p_{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

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# Terminology question

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