答：
1.
f'(x)=333x^332g(x)+(x^333-1)g'(x)+(4-4lnx)/x^2.
f'(x)=333g(1)+4
=333*6+4
=2002
2.原式
=d[f(ax+b)]*a/d(ax+b)
将ax+b看成t,上式=a*d[f(t)]/dt=a*g(t)
=a*g(ax+b)
3.
设d[f(x)]/dx=g(x),同上题.
d[f(x^2)]/dx
=d[f(x^2)]*2x/d(x^2)
=2x*g(x^2)
4.
f(t)=limx->+∞ [t(1+t/x)^tx]
=limx->+∞ t[(1+1/(x/t))^(x/t*t^2)]
=te^(t^2)
所以f'(t)=e^(t^2)+2t^2*e^(t^2)
=e^(t^2)*(1+2t^2)