How to apply the definition of the derivative of a delta function

rocky3321
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I am supposed to prove that δ'(ax) = (1/a)*(1/|a|)*δ'(x) but I cannot figure out where the (1/a) term comes from. Using the scaling theorem I know that δ(ax) = (1/|a|)*δ(x), but how does this apply to the first derivative and does it explain where the (1/a) comes from?
 
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No need to post any further dialogue because I was able to figure it out. Thanks
 
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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