Question

How do you find the derivative of a power series?

Answer 1

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.