Derivative of a Multivariable Function from Definition in Vector Spaces

samer88
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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


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The Attempt at a Solution

 
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The derivative or derivatives? If it is the derivatives just take the partial derivatives inside the vector
 
no it is the derivative
 
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:-(
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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