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

#f(x)=sum_{n=0}^inftyc_nx^n#,

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.