Generalization of the product rule to the nth derivative

madah12
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Homework Statement



do what the title says

Homework Equations





The Attempt at a Solution


ok so I think it's
h(x)=f(x)g(x)
sum from k=0 to n of (n choose k) f^(n-k)(x) g^(k)(x)
right?
 
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Yes, that is correct.
 
Does it work for n=2? Not too hard to check ...
 

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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