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.)

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Answer 2

To find the derivative of a power series, you differentiate each term of the series individually. This process involves applying the rules of differentiation to each term, considering that a power series is an infinite sum of terms. The derivative of each term can be found using standard differentiation rules, such as the power rule or the chain rule, depending on the form of the term. After differentiating each term, you obtain a new series representing the derivative of the original power series.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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