Question

Can someone explain how do I use derivatives and integrals to find a power series representation of a function

Answer 1

For example, I have to find a power series rep of ln(1+x^4) I can take the derivative of this and get 4/(1+x^4) which is in the form for the power series x^n. My question is do I plug in -x^4 for x and multiply it by 4, then take the derivative of the series or do i take the derivative of the series and then plug in -x^4 and multiply by 4? OR if i take the derivative of something in order to get a power series do I then take the integral of the series x^n? I am confused!