I was trying to solve a differentiation question but unable to understand .
My question is :
find the $n^{th}$ derivative of $1/(1+x+x^2+x^3)$
I know that if we divide the numerator by denominator then the expression would be :
$1- x(1+ x^2 + x )/(1+x+x^2+x^3)$
But now how to find the nth derivative?
Please somebody explain this..
Thanx 🙂
Best Answer
HINT:
Use Partial Fraction Decomposition
$$\frac1{1+x+x^2+x^3}=\frac1{(x+1)(x^2+1)}=\frac A{x+1}+\frac B{x+i}+\frac C{x-i}$$