I have u(t) which is an function of t, and g(u) which is a function of u. I want to find the derivative of g(u)*u(t) w.r.t. t.
sage: u(t) = function('u')(t)
sage: h(u) = function('h')(u)
sage: u
u
sage: h
u |--> h(u)
diff(h(u)*u(t),t)
h(u)
This seems to happen because the function u is overwritten when I use u to define the function h. I can get around it this way.
sage: u(t) = function('u')(t)
sage: h(x) = function('h')(x)
sage: u
t |--> u(t)
sage: h
x |--> h(x)
sage: diff(h(u)*u(t),t)
u(t)*D[0](h)(u(t))*D[0](u)(t) + h(u(t))*D[0](u)(t)
Can this be classified as a bug? If it is, would it be possible to fix it?
