f(x)=1/[(x+1)In(x+1)]的导函数是什么?
问题描述：
f(x)=1/[(x+1)In(x+1)]的导函数是什么?
答
f'=-[ln(x+1)+1]/[(x+1)In(x+1)]^2
答
f(x)'=[1+ln(x+1)]/[(x+1)ln(x+1)]^2
答
f'(x)={[1/(x+1)][1/ln(x+1)]}'=[1/(x+1)]'[1/ln(x+1)]+[1/(x+1)][1/ln(x+1)]'=-1/[(x+1)²ln(x+1)]+[1/(x+1)][-1/ln²(x+1)][1/(x+1)]=-1/[(x+1)²ln(x+1)]-1/[(x+1)²ln²(x+1)]=-[ln(x+1)+1]...
答
f'(x)=-[1+ln(x+1))]/[(x+1)In(x+1)]^2