Let f (x) = (1 + x) ^ 6 (1-x) ^ 5, then what is the coefficient of x ^ 3 in F '(x)?

Let f (x) = (1 + x) ^ 6 (1-x) ^ 5, then what is the coefficient of x ^ 3 in F '(x)?

(1+x)^6(1-x)^5
=(1+x)(1+x)(1+x)(1+x)(1+x)(1+x)(1-x)(1-x)(1-x)(1-x)(1-x)
=(1-x^2)(1-x^2)(1-x^2)(1-x^2)(1-x^2)(1+x)
=(1-2x ^ 2 + x ^ 4) (1-2x ^ 2 + x ^ 4) + (1-x ^ 2x-x ^ 3) (these two steps
=(1-4x ^ 2 + 6x ^ 4-4x ^ 6 + x ^ 8) (1-x ^ 2x-x ^ 3) can be omitted)
=1-5x^2-5x^3+10x^4+10x^5-10x^6-10x^7+5x^8+5x^9-x^10-x^11
So the coefficient of x ^ 3 in F (x) is - 5

Elden Ring Premiere

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