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1. y = (1+x)(2+3x)^2 (4+5x)^3 = (4+16x+21x^2+9x^3)(4+5x)^3
= (9*5^3)x^6 + (21*5^3+9*300)x^5 +......
y^(5)(0) = (21*5^3+9*300) 5! = 639000.
2. y = x^6 (x^2+1)^3 (x+2)^2
y' = 6x^5 (x^2+1)^3 (x+2)^2 + x^6[3(x^2+1)^2*2x] (x+2)^2 + x^6 (x^2+1)^3[2(x+2)]
= 2x^5 (x+2)(x^2+1)^2 [3(x^2+1)(x+2) + 3x^2(x+2) + x(x^2+1)]
= 2x^5 (x+2)(x^2+1)^2 (7x^3+12x^2+4x+6)
= (9*5^3)x^6 + (21*5^3+9*300)x^5 +......
y^(5)(0) = (21*5^3+9*300) 5! = 639000.
2. y = x^6 (x^2+1)^3 (x+2)^2
y' = 6x^5 (x^2+1)^3 (x+2)^2 + x^6[3(x^2+1)^2*2x] (x+2)^2 + x^6 (x^2+1)^3[2(x+2)]
= 2x^5 (x+2)(x^2+1)^2 [3(x^2+1)(x+2) + 3x^2(x+2) + x(x^2+1)]
= 2x^5 (x+2)(x^2+1)^2 (7x^3+12x^2+4x+6)
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