If $\dfrac{dy}{dt} = 2$ and $\dfrac{dt}{dx}=5$, then chain rule gives $\dfrac{dy}{dx}=2*5=10$.
However if we define $\dfrac{dy}{dt}=2$ to be the speed of a person in a moving train relative to train,
and $\dfrac{dt}{dx}=5$ to be the speed of train relative to ground, this gives speed of person relative to ground as $\dfrac{dy}{dx}=2+5=7$.
I feel I'm missing something.. Any help?
If you define $ \frac{dy}{dt} $ as the speed of a person relative to the train, you define that persons position $ y $ relative to the train as a function of $ t $.
The trains speed relative to the ground cannot be defined as $ dt / dy $, it would make no sense to define the trains time $ t $ as a function of the persons position $ y $.
Rather define the speed of the train as $ \frac{dy'}{dt} $, where $ y' $ is the trains position relative to the ground.
Then the persons speed is, (without taking relativity into account),
$$ \frac{dy}{dt} + \frac{dy'}{dt} $$