设f(x)=(tan(π/4)x-1)(tan(π/4)x²-2).(tan(π/4)x^100-100),求

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设f(x)=(tan(π/4)x-1)(tan(π/4)x²-2).(tan(π/4)x^100-100),求f'(1)

tan(π/4)=1
f(x)=(x-1)(x^2-2)...(x^100-100)
y=uv,y'=u'v+uv'
y=uvw,y'=(uv)'w+uvw'=u'vw+uv'w+uvw'
f'(x)除了(x-1)'(x^2-2)...(x^100-100)其它各项都有因式(x-1)
所以f'(1)=(1^2-2)(1^3-3)...(1^100-100)
=(-1)(-2)...(-99) 共99项
=-99!
负的99阶乘

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