How do you find the derivative of a power series?

1 Answer
Oct 2, 2014

One of the most useful properties of power series is that we can take the derivative term by term. If the power series is


then by applying Power Rule to each term,

#f'(x)=sum_{n=0}^infty c_n nx^{n-1}=sum_{n=1}^inftync_nx^{n-1}#.

(Note: When #n=0#, the term is zero.)

I hope that this was helpful.