On Saturday, November 2, 2013 5:48:30 PM UTC+1, Aaron Meurer wrote:
>
> But in general, you can't invert formulas (and even if you 
> mathematically can, it doesn't mean that solve() can do it). 
>
>
I was just thinking about this, and about the more general case where you 
are deriving by unknown expression.

I suggest that in such cases the differentiation returns an unevaluated 
derivative.

It would be nice to handle derivation by another function, for example:

>>> x.diff(f(x))
Derivative(x, f(x))
>>> x.diff(f(y))
Derivative(x, f(y))
>>> f(x).diff(g(x))
Derivative(f(x), g(x))
>>> f(x).diff(g(y))
Derivative(f(x), g(y))

At least, I would start be leaving the derivative unevaluated, so in the 
future it will be easier to add tools to handle functional derivatives.

Saullo, do you think you can add something like this?
 

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