# Differentiating power series

EV33
My question is just a concept that I don't understand.

When differentiating a power series that starts at n=0 we bump that bound up to n=1.

My question is do we always do that?

or

Do we only do that when the first term of the power series is a constant and thus when it is differentiated it becomes zero?

My guess is the second case.

## Answers and Replies

Jamin2112
My question is just a concept that I don't understand.

When differentiating a power series that starts at n=0 we bump that bound up to n=1.

My question is do we always do that?

or

Do we only do that when the first term of the power series is a constant and thus when it is differentiated it becomes zero?

My guess is the second case.

Huh? n = 0 is just the index. We can call out "starting point" a0 or a1 --- whichever we prefer. And yes, that term will disappear when you take the derivative of ∑anxn.

a0 + a1x + a2x2 + ...

(a0 + a1x + a2x2 + ... )' = a1 + 2a2x + ...

It's as simple as that.