y=ln(x+根号1+x的平方)和y=ln根号1+sinx分之1-sinx的导数

∵ f(x)+f(-x)
= lg[x+√(1+x^2)] + lg[-x+√(1+(-x)^2)]
= lg {[x+√(1+x^2)]×[-x+√(1+x^2)]}
= lg {[√(1+x^2)+x]×[√(1+x^2)-x]}
= lg 1
= 0
∴ f(-x) = -f(x)
f(-a) = -f(a) = -

y=f(x)=lg(x+√ (x^2+1))
f(-x)=lg[-x+√ (x^2+1)]
=lg[√ (x^2+1))-x]
=lg{1/[√ (x^2+1))+x]}
=lg[√ (x^2+1))+x]^(-1)
=-lg[√ (x^2+1))+x]
=-lg[x+√ (x^2+1)]
=-f(x)
∴函数y=lg(x+√ (x^2+1))为奇函数.

x=(1/2)[5^(1/n)-5^(-1/n)]
1+x²=1+(1/4)[5^(2/n)-2+5^(-2/n)]
=(1/4)[5^(2/n)+2+5(-2/n)]
=(1/4)[5^(1/n)+5^(-1/n)]²
所以√(1+x²)=(1/2)[5^(1/n)+5^(-1/n)]
故（x+根号1+x的平方)^n
=[5^(1/n)]^n
=5