power rule:
(deltay)/(deltax) x^n = nx^(n-1)
when an expression x^n is differentiated, the result will have a degree 1 less than that of the original.
e.g. (deltay)/(deltax) x^7 = 7x^6
if this rule is used for each stage of the derivative, the 4th derivative will have a degree 4 less than that of the original expression.
(deltay)/(deltax) x^7 = 7x^6
(delta^2y)/(deltax^2) x^7 = 42x^5
(delta^3y)/(deltax^3) x^7 = 210x^4
(delta^4y)/(deltax^4) x^7 = 840x^3
the fourth derivative of x^7 has a degree 4 lower than x^7 does.
(delta^4y)/(deltax^4) x^7 = 840x^(7-4)
if a polynomial is 7th degree, the highest degree is 7.
the highest degree of the fourth derivative would therefore be 7-4, which is 3.