Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\frac{dw}{dt}$ is equal to

- $\frac{dw}{dx} \frac{dx}{dt} + \frac{dw}{dy} \frac{dt}{dt}$
- $\frac{\partial w}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial w}{ \partial y} \frac{\partial y}{ \partial t}$
- $\frac{\partial w}{\partial x} \frac{d x}{dt} + \frac{\partial w}{ \partial y} \frac{dy}{dt}$
- $\frac{d w}{dx} \frac{\partial x}{\partial t} + \frac{dw}{dy} \frac{\partial y}{ \partial t}$