Question

已知f(x)=(x+1)(x+2)(x+3)……（x+100),求（f(x))的导数

Answer 1

f（x)=（x＋1）（x＋2）（x＋3）．．．．．．（x＋100）,

lnf(x)=ln(x+1)+ln(x+2)+...+ln(x+100)

ln'f(x)=f'(x)/f(x)=1/(x+1)+1/(x+2)+.+1/(x+100)

f'(x)=f(x)*[1/(x+1)+1/(x+2)+...+1/(x+100)]