Question

求导数的问题谢谢了

Answer 1

由导数的定义直接可以算出来，结果可导，希望帮到你，不懂可以追问

Answer 2

f(x)
=ln(1+x^2)/x ; x≠0
=0 ; x=0
lim(x->0) ln(1+x^2)/x (0/0 分子分母分别求导)

=lim(x->0) 2x/(1+x^2)
=0
=f(0)
x=0, f(x) 连续
f'(0)
=lim(h->0) [f(1+h^2) - f(0) ]/h
=lim(h->0) ln(1+h^2) /h^2
=lim(h->0) h^2/h^2
=1
x≠0

f(x)=ln(1+x^2)/x
f'(x)
= 2x/[x(1+x^2)] - ln(1+x^2)/x^2
= 2/(1+x^2) - ln(1+x^2)/x^2
ie
f'(x)
= 2/(1+x^2) - ln(1+x^2)/x^2 ;x≠0
=1 ; x=0