# How do you find the #n#-th derivative of a power series?

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To find the n-th derivative of a power series, you can use term-by-term differentiation. Given a power series ( f(x) = \sum_{n=0}^{\infty} a_n x^n ), where ( a_n ) are the coefficients, the n-th derivative of ( f(x) ) is ( f^{(n)}(x) = \sum_{n=0}^{\infty} a_n (n)(n-1)...(n-(n-1)) x^{n-n} ) or simply ( f^{(n)}(x) = \sum_{n=0}^{\infty} a_n (n)(n-1)...(n-(n-1)) x^0 ).

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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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