I see it like F = d/dt (mv) as the (time) rate of change of mv . But that can also be expressed as d(mv)/dt - it's just a notion. Because M is constant (in newton mechanics) then:
d(mv) = M x dv, as the product is constant, as M is constant.
(1) The full derivative with respect to time (which I think can be written with capital (D/Dt) or lowercase (d/dt). Because the material property is a function of space and time, with D/Dt we assume that a particle is being followed so x y and z depend on time.
and
(2) The partial derivative with respect to time, which would be written with the partial derivative symbol rather than d or D.
can you explain it in terms of current flow into a capacitor? {i = C * dv/dt} yet {i(t) = C * d/dt * v(t)} fluid mechanics make alot of good analogies for electronics. if dt is a time iterval then what is the d ?
I would say that the two equations you wrote are equivalent. You can think of d/dt as a symbol that just means "take the derivative with respect to t." Another way to think of it is dv divided by dt, where if you are at time t and you take a very small step in time, called dt, then the value of the function v will change by dv when you take that step.
I see it like F = d/dt (mv) as the (time) rate of change of mv . But that can also be expressed as d(mv)/dt - it's just a notion. Because M is constant (in newton mechanics) then:
d(mv) = M x dv, as the product is constant, as M is constant.
And from them you see dv/dt as A.
clearlyasexyboy 1 year ago
Note:
This video is about the difference between
(1) The full derivative with respect to time (which I think can be written with capital (D/Dt) or lowercase (d/dt). Because the material property is a function of space and time, with D/Dt we assume that a particle is being followed so x y and z depend on time.
and
(2) The partial derivative with respect to time, which would be written with the partial derivative symbol rather than d or D.
explainseries 3 years ago
can you explain it in terms of current flow into a capacitor? {i = C * dv/dt} yet {i(t) = C * d/dt * v(t)} fluid mechanics make alot of good analogies for electronics. if dt is a time iterval then what is the d ?
rshfn44 3 years ago
I would say that the two equations you wrote are equivalent. You can think of d/dt as a symbol that just means "take the derivative with respect to t." Another way to think of it is dv divided by dt, where if you are at time t and you take a very small step in time, called dt, then the value of the function v will change by dv when you take that step.
explainseries 3 years ago
...derive with respect to t
Krisspychiken 3 years ago
differentiate. you're not deriving anything
hxc7273 3 years ago
man.....plz tell me u ain't a teacher
aeelsherif 3 years ago
advice: take some rhetoric lessons
frostwow 4 years ago