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pythonsympyderivative

Distribute derivative of sum with constant term after substitution

If I do

import sympy
k, V, Vprime = sympy.symbols('k, V, Vprime')

print sympy.diff(k + V(t), t)

I get Derivative(V(t), t) as I expect - the derivative distributes and the constant term has zero derivative.

However, if I construct an equivalent expression via substitution, simplify does not distribute the derivative. How can I get the same result via substitution as when I evaluate the expression directly?

sympy.diff(Vprime(t)).subs({Vprime(t): k + V(t)}).simplify()

returns Derivative(k + V(t), t).

Solution

  • The solution to this problem is provided by the doit method, which says it "Evaluate(s) objects that are not evaluated by default like limits, integrals, sums and products.":

    sympy.diff(Vprime(t)).subs({Vprime(t): k + V(t)}).doit()

    yields

    Derivative(V(t), t)