Given the function y = x (x-1) &# 178; (x + 3) &# 179;, find y ^ (6)

Given the function y = x (x-1) &# 178; (x + 3) &# 179;, find y ^ (6)

y=x(x-1)^2(x+3)^3
Let y = ax ^ 6 + BX ^ 5 + CX ^ 4 + DX ^ 3 + ex ^ 2 + FX + G
Then after the sixth derivative, all the following become 0
So y '' = (AX ^ 6) '"
In the expansion, the coefficient of the sixth power of X is 1,
So: y ^ (6) = (x ^ 6) '"
(x^6)'=6x^5
(x^6)''=6*5*x^4
Original formula = 6 * 5 * 4 * 3 * 2 * 1 = 30 * 6 * 4 = 180 * 4 = 720

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