# Finding total derivative of a multivariate function in Maple

In Maple, I have a function $$f(x(t),y(t),t)$$ that I want to differentiate with respect to $$t$$. I know the command for partial derivative $$\frac{\partial f}{\partial x}$$,$$\frac{\partial f}{\partial y}$$,$$\frac{\partial f}{\partial t}$$, etc in Maple. But I can't find a way to find total derivative $$\frac{df}{dt}$$.

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• So just do it explicitly Nov 24 at 15:54
• Have you tried the diff from the Physics package? Nov 25 at 2:13

You have this function:

$$f = f(x,y,t)$$

so:

$$df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy + \frac{\partial f}{\partial t} dt$$

or:

$$\frac{df}{dt} = \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y} \frac{dy}{dt} + \frac{\partial f}{\partial t}$$

You said that, you are able to calculate $$\frac{\partial f}{\partial x}$$, $$\frac{\partial f}{\partial y}$$, and $$\frac{\partial f}{\partial t}$$. So, just calculate them and I assume you know the relations of $$x = x(t)$$, $$y = y(t)$$ as well. So, everything is ready to find the $$\frac{df}{dt}$$ here.

• Thanks, but I need a general symbol for this in MAPLE. I need to find total derivatives several times. Doing the manual process is not feasible. Nov 24 at 20:25
• @ilawid I worked with Maple many years ago, but I believe it should be easy to automate this process. Basically it's a function that you put your symbolical $f$, $x=x(t)$, and $y=y(t)$ into it and it just calculates $\partial_{x} f$, $\partial_{y} f$, $\partial_{t} f$, $\dot{x}$, and $\dot{y}$ and returns $\dot{f}$ based on that formula. I'm not sure why you think you need to do it manually. Note: at the end $\dot{f}$ might not be something really compact or even it's not guaranteed that you would be able to write it down based on only $t$ parameter. It just depends on explicit formula of $f$. Nov 24 at 20:50