Total derivative

Total derivatives are often written as $\frac{df}{dt}$, not to be confused with a Partial Derivative .

• Write why this differs from the Partial Derivative

Derivation rules

$$\begin{array}{rll}(f\circ g{)}^{\prime }& =(f^{\prime }\circ g)\times g^{\prime }& \text{Composition rule}\\ (fg{)}^{\prime }& =f^{\prime }g+g^{\prime }f& \text{Product rule}\\ {\left(\frac{f}{g}\right)}^{\prime }& =(f^{\prime }g-g^{\prime }f)g^{-2}& \text{Quotient rule}\end{array}$$