There is a theorem in partial derivative(adsbygoogle = window.adsbygoogle || []).push({});

If x= x(t) , y= y(t), z= z(t) are differentiable at [tex]t_{0}[/tex], and if w= f(x,y,z) is differentiable at the point (x,y,z)=(x(t),y(t),z(t)),then w=f(x(t),y(t),z(t)) is differentiable at t and

[tex]\frac{dw}{dt}[/tex]=[tex]\frac{\partial w}{\partial x}[/tex][tex]\frac{dx}{dt}[/tex] + [tex]\frac{\partial w}{\partial y}[/tex] [tex]\frac{dy}{dt}[/tex] + [tex]\frac{\partial w}{\partial z}[/tex] [tex]\frac{dz}{dt}[/tex]

where the ordinary derivatives are evaluated at t and the partial derivatives are evaluated at (x,y,z)

My question are

1. What is the difference between dx and[tex]\partial x[/tex]?

2. i don't know why i am not allowed to eliminate the dx and [tex]\partial x[/tex],also the same for y and z to get 3[tex]\frac{\partial w}{dt}[/tex]

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# Chain rule in partial derivative

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