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  • https://math.libretexts.org/Courses/Montana_State_University/M273%3A_Multivariable_Calculus/14%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/The_Chain_Rule_for_Functions_of_Multiple_Variables
    \[\begin{align*} \dfrac{∂w}{∂t} =\dfrac{∂w}{∂x}\dfrac{∂x}{∂t}+\dfrac{∂w}{∂y}\dfrac{∂y}{∂t}+\dfrac{∂w}{∂z}\dfrac{∂z}{∂t} \\[4pt] \dfrac{∂w}{∂u} =\dfrac{∂w}{∂x}\dfrac{∂x}{∂u}+\dfrac{∂w}{∂y}\dfrac{∂y}{∂u...wt=wxxt+wyyt+wzztwu=wxxu+wyyu+wzzuwv=wxxv+wyyv+wzzv.
  • https://math.libretexts.org/Courses/Misericordia_University/MTH_226%3A_Calculus_III/Chapter_14%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/3.10%3A_The_Chain_Rule_for_Functions_of_Multiple_Variables
    \[\begin{align*} \dfrac{∂w}{∂t} =\dfrac{∂w}{∂x}\dfrac{∂x}{∂t}+\dfrac{∂w}{∂y}\dfrac{∂y}{∂t}+\dfrac{∂w}{∂z}\dfrac{∂z}{∂t} \\[4pt] \dfrac{∂w}{∂u} =\dfrac{∂w}{∂x}\dfrac{∂x}{∂u}+\dfrac{∂w}{∂y}\dfrac{∂y}{∂u...wt=wxxt+wyyt+wzztwu=wxxu+wyyu+wzzuwv=wxxv+wyyv+wzzv.
  • https://math.libretexts.org/Courses/Georgia_State_University_-_Perimeter_College/MATH_2215%3A_Calculus_III/14%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/The_Chain_Rule_for_Functions_of_Multiple_Variables
    \[\begin{align*} \dfrac{∂w}{∂t} =\dfrac{∂w}{∂x}\dfrac{∂x}{∂t}+\dfrac{∂w}{∂y}\dfrac{∂y}{∂t}+\dfrac{∂w}{∂z}\dfrac{∂z}{∂t} \\[4pt] \dfrac{∂w}{∂u} =\dfrac{∂w}{∂x}\dfrac{∂x}{∂u}+\dfrac{∂w}{∂y}\dfrac{∂y}{∂u...wt=wxxt+wyyt+wzztwu=wxxu+wyyu+wzzuwv=wxxv+wyyv+wzzv.

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