Total Derivatives and Total Differential I am confused between total derivatives and total differential. What is  the difference between total derivatives and 
total differential?

Let $f: U \subset \Bbb R^n \to \Bbb R^m$ be differentiable. 
The total derivative of $f$ at $a$ is the linear map $df_a$ such that $f(a+t) - f(a) = df_a(t) + o(t)$. 
For $m=1$, the total differential of $f$ is
$$df = \sum_{i=1}^m \frac{\partial f}{\partial x_i} dx_i$$
Hope this helps.
