已知f(x)=x(x+1)(x+2)(x+3)(x+4)(x+5)+6,则f′(0)=______.
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已知f(x)=x(x+1)(x+2)(x+3)(x+4)(x+5)+6,则f′(0)=______.
![已知f(x)=x(x+1)(x+2)(x+3)(x+4)(x+5)+6,则f′(0)=______.](/uploads/image/z/14890475-11-5.jpg?t=%E5%B7%B2%E7%9F%A5f%EF%BC%88x%EF%BC%89%3Dx%EF%BC%88x%2B1%EF%BC%89%EF%BC%88x%2B2%EF%BC%89%EF%BC%88x%2B3%EF%BC%89%EF%BC%88x%2B4%EF%BC%89%EF%BC%88x%2B5%EF%BC%89%2B6%EF%BC%8C%E5%88%99f%E2%80%B2%EF%BC%880%EF%BC%89%3D______%EF%BC%8E)
∵f(x)=x(x+1)(x+2)(x+3)(x+4)(x+5)+6,
∴f′(x)=(x+1)(x+2)(x+3)(x+4)(x+5)+x(x+2)(x+3)(x+4)(x+5)+x(x+1)(x+3)(x+4)(x+5)+x(x+1)(x+2)(x+4)(x+5)+x(x+1)(x+2)(x+3)(x+5)+x(x+1)(x+2)(x+3)(x+4),
∴f′(0)=1×2×3×4×5=120.
故答案为120.
∴f′(x)=(x+1)(x+2)(x+3)(x+4)(x+5)+x(x+2)(x+3)(x+4)(x+5)+x(x+1)(x+3)(x+4)(x+5)+x(x+1)(x+2)(x+4)(x+5)+x(x+1)(x+2)(x+3)(x+5)+x(x+1)(x+2)(x+3)(x+4),
∴f′(0)=1×2×3×4×5=120.
故答案为120.
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