例3设f(x)=x(x+2)(x+4)……(x+2n),求f(0)的导数。
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令g(x)=x(x+2)……(x+2n)f(x)=x*g(x)f'(x)=x'*g(x)+x*g'(x)=g(x)+x*g'(x)f'(0)=g(0)+0*g'(x)=g(0)=0(0+2)*(0+4)*.(0+2n)=0
咨询记录 · 回答于2023-02-26
例3设f(x)=x(x+2)(x+4)……(x+2n),求f(0)的导数。
令g(x)=x(x+2)……(x+2n)f(x)=x*g(x)f'(x)=x'*g(x)+x*g'(x)=g(x)+x*g'(x)f'(0)=g(0)+0*g'(x)=g(0)=0(0+2)*(0+4)*.(0+2n)=0
g(x)应该没有乘x吧
令g(x)=(x+2)……(x+2n)f(x)=x*g(x)f'(x)=x'*g(x)+x*g'(x)=g(x)+x*g'(x)f'(0)=g(0)+0*g'(x)=g(0)=(0+2)*(0+4)*.(0+2n)=2×4……×2n=2n!