Minimum value of n for non-zero 4th derivative in Euler-Bernoulli beam equation

Huumah
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Prove that this equation satifies the Euler-bernoulli beam equation which is given by

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Cany anyone help me with this. Can wolfram alpha do it? It has so many values and I'm not comfartble with doing 4th derivitives
 
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You don't have to do all the derivatives. If you have some term like ax^n, where a is a constant, what is the min value of n so that the 4-th derivative is not zero? What is its value in the min case?
 

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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