Question

函数Y=Ln(1+x),求d的n次方y/dx的n次方

Answer 1

Dy/Dx=1/(1+x)

D^2y/Dx^2=-1/(1+x)^2

D^3y/Dx^3=-2*(-1/(1+x)^3)=2/(1+x)^3

D^4y/Dx^4=-3*(2/(1+x)^4)=-6/(1+x)^4

所以

D^ny/Dx^n=(-1)^(n+1)*(n-1)(n-2)/(1+x)^n