第1个回答 2019-04-16
ln(1+x^2)^(2/x)
=(2/x)ln(1+x^2)
f(x)
=ln(1+x^2)^(2/x) ; x≠0
=0 ; x=0
lim(x->0) ln(1+x^2)^(2/x)
=lim(x->0) 2ln(1+x^2)/x (0/0 分子分母分别求导)
=lim(x->0) 4x/(1+x^2)
=0
=f(0)
x=0 , f(x) 连续
f'(0)
=lim(h->0) [ ln(1+h^2)^(2/h) -f(0) ]/ h
=lim(h->0) ln(1+h^2)^(2/h) / h
=lim(h->0) 2ln(1+h^2) / h^2
=lim(h->0) 2h^2/ h^2
=2
ie
f'(x)
=-(2/x^2).ln(1+x^2) - 4/(1+x^2) ; x≠0
=2 ; x=0