Total derivative without specified function

Question

How to take total derivative if I don't have a function?

For example $$ u=f(t),\ \ when \ \ t = x+y $$

I assume that it's something like $$ du = \frac{∂u}{∂t}*dt $$ but how do we use information about t value?

Answer 1

Derivative of f should be known, say g: $$ du = \frac{d f(t)}{dt} (dx + dy) =g(t)(dx + dy)=g(x+y)(dx + dy) $$