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Is there a way to define in Mathematica a generic differentiable function $g:\mathbb{R}^2\rightarrow \mathbb{R}$ in such a way that when it computes the derivatives of a composed function involving $g$ it leaves indicated the derivatives of $g$ instead of actually computing them?

I'll explain myself better with an example:

Suppose we have defined this "generic" $g:\mathbb{R}^2\rightarrow \mathbb{R}$ and we have defined $F:\mathbb{R}\rightarrow \mathbb{R}$, $F(x)=7Log[x]$. When given the command $D(F(g(x,y)),x)$ I would like to have the output $7\partial_x(g)/g$. Is it possible?

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    – user9660
    Oct 25, 2016 at 15:11

1 Answer 1

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It is not only possible, it is actually quite straightforward. Define f in the usual way:

f[x_] := 7 Log[x]

Then take the derivative of the composition with g[x,y] (being an "undefined" generic function). The answer is as you expect:

D[f[g[x, y]], x]

enter image description here

So there is no need to specially define the function g[x,y].

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