若f(x)=(x+1)(x+2)…(x+10),求f(x)的9次导数?

问题描述:

若f(x)=(x+1)(x+2)…(x+10),求f(x)的9次导数?

lnf(x)=ln(x+1)+ln(x+2)+.+ln(x+10)
两边求导得到
f'(x)/f(x)=1/(x+1)+1/(x+2)+.+1/(x+10)
所以
f'=f(x)*[1/(x+1)+1/(x+2)+.+1/(x+10)]9�ε��� ����ԭʽ=x^10+55x^9+a1x^8+....+a8x+a9��Ŵε���˴����µĶ�����0����f'(9)=10�Ľ׳�*x+55*9�Ľ׳�=9�Ľ׳�(10x+55)