作业帮f(x)=(x+1)(2x+1)(3x+1).(nx+1),求f'(0)
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f(x)=(x+1)(2x+1)(3x+1).(nx+1),求f'(0)
f(x)=(x+1)(2x+1)(3x+1)....(nx+1),求f'(0)万分感谢
f(x)=(x+1)(2x+1)(3x+1)....(nx+1),求f'(0)万分感谢
f(x)=y=(x+1)(2x+1)(3x+1).(nx+1),求f'(0)
两边取自然对数得：lny=ln(x+1)+ln(2x+1)+ln(3x+1)+.+ln(nx+1)
两边对x取导数得y'/y=1/(x+1)+2/(2x+1)+3/(3x+1)+.+n/(nx+1)
故f'(x)=f(x)[1/(x+1)+2/(2x+1)+3/(3x+1)+.+n/(nx+1)]
∴f'(0)=f(0)(1+2+3+.+n)=f(0)(1+n)n/2
因为f(0)=1,故f'(0)=n(n+1)/2.
两边取自然对数得：lny=ln(x+1)+ln(2x+1)+ln(3x+1)+.+ln(nx+1)
两边对x取导数得y'/y=1/(x+1)+2/(2x+1)+3/(3x+1)+.+n/(nx+1)
故f'(x)=f(x)[1/(x+1)+2/(2x+1)+3/(3x+1)+.+n/(nx+1)]
∴f'(0)=f(0)(1+2+3+.+n)=f(0)(1+n)n/2
因为f(0)=1,故f'(0)=n(n+1)/2.
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