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

  1. $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$
  2. $\dfrac{\partial w}{\partial x} \dfrac{\partial x}{\partial t} + \dfrac{\partial w}{ \partial y} \dfrac{\partial y}{ \partial t} \\$
  3. $\dfrac{\partial w}{\partial x} \dfrac{d x}{dt} + \dfrac{\partial w}{ \partial y} \dfrac{dy}{dt} \\$
  4. $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
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