Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium

New issue 3582 by [email protected]: The chain rule should take derivatives with respect to functions when it can
http://code.google.com/p/sympy/issues/detail?id=3582

As reported on the mailing list:

    x=Symbol('x')
    y=Symbol('y')
    t=Symbol('t')
    f=Function('f')
    u=f(x,t)

    phi=Function('phi')

    Phi = phi(x,t,u)

    part=Phi
    total=diff(part,x)

    print total

Derivative(f(x, t), x)*Subs(Derivative(phi(x, t, _xi_3), _xi_3), (_xi_3,), (f(x, t),)) + Derivative(phi(x, t, f(x, t)), x)

The answer should contain the derivative with respect to the function f(x, t). Furthermore, Subs.doit() should make this replacement.

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