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

[Huumah]

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

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

 

[voko]

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?