Derivative of a Multivariable Function from Definition in Vector Spaces

[samer88]

Homework Statement

determine the derivative of f(x,y,z)=(x^2-2xy+z,y^2+z^2) directly from the definition where f:R^3------->R^2

Homework Equations

The Attempt at a Solution

 

[MaxManus]

The derivative or derivatives? If it is the derivatives just take the partial derivatives inside the vector

 

[samer88]

no it is the derivative

 

[MaxManus]

And it does not say with respect to what?
I would guess taking all the first derivatives
f(x,y,z)=(x^2-2xy+z,y^2+z^2)
f'(x) = (2x-2y,0)
f'(y) = (-2x,2y)
f'(z) = (1,2z)
But I guess the question is to advanced for me:-(