
Arturo O. answered 09/04/18
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Student,
Not TRUE in general. Example:
z(x,y) = x2 - 3y
∂z/∂y = -3 = scalar

Arturo O.
If it is a scalar function, the total derivative is a scalar. For example, consider
f = f(x(t), y(t), t)
df/dt = (∂f/∂x)(dx/dt) + (∂f/∂y)(dy/dt) + ∂f/∂t
But you could also have a vector function F whose total derivative is also a vector.
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