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How to find the Jacobi-Matrix for the following functions?

$f:(x,y)\rightarrow x^2+y^2$

$f: (x,y)\rightarrow \sqrt{x^2+y^2}$

$f:\mathbb{R}^n\rightarrow \mathbb{R}: x\rightarrow \sum_{i=1}^nx_i^2$

$f:\mathbb{R}^n\rightarrow \mathbb{R}: x\rightarrow ||x||_2$

For the first one I have an idea, but for the others I have no idea. Can someone provide me with a solution/hint/Source where I can find more on this kind of problems?

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    The third and fourth are generalizations of the first and second – 2017-01-15
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    yes, thats right. So in fact I have to solve the last two, right? – 2017-01-15
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    IMHO you should first solve the first and the second. It would help you understand the general case. Something else : do you know how the Jacobi matrix of a map at some point is defined ? – 2017-01-15

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