Definition
Differential: how does a function's value change when its independent variable has a minimum change. We denote the change
as dy.
For function in one-dimension, we have the relationship between differential (dy, dx) and derivative (f'(x)) as:
Basic differential rule
Let u and v to be two differentiable functions, we have:
- d(au + bv) = dau + dbv = adu + bdv
- d(uv) = udv + vdu

- If y(u) is derivable, d[y(u)] = y'(u)du
Differential of inverse function
If f is differentiable, then
is also differentiable: