Question

导数已知f(x)=x(x+1)(x+2)...(x+2005),f'(x)

Answer 1

y=f(x)=x(x+1)(x+2)...(x+2005)

lny=lnx+ln(x+1)+……+ln(x+2005)

y'/y=1/x+1/(x+1)+……+1/(+2005)

f'(x)=y'=y*[1/x+1/(x+1)+……+1/(+2005)]

=x(x+1)(x+2)...(x+2005)*[1/x+1/(x+1)+……+1/(+2005)]

=(x+1)(x+2)...(x+2005)+x(x+2)...(x+2005)+……+x(x+1)(x+2)...(x+2004)