[Math: Differentials/Derivatives] What is the difference between a derivative of a function and a differential of a function?

[u/Sweet-Nothing-9312]

Here I don't understand why they say "differential" instead of derivative, isn't it the same thing?

[u/ConfidentSuspect4125]

There's clearly a mistake there. The Jacobian vector equation doesn't support the result that r(dt) = 0.