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

One of the most useful properties of power series is that we can take the derivative term by term. If the power series is

then by applying Power Rule to each term,

I hope that this was helpful.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you find a power series representation for #x/(1-x^2)# and what is the radius of convergence?
- How do you use a Taylor series to expand: #f(x) = x^2 + 2x + 5# about x = 3?
- What is the Maclaurin series for? : #1/root(3)(8-x)#
- What is the interval of convergence of #sum_1^oo sin((pi*n)/2)/n^x #?
- How do you find a power series converging to #f(x)=e^(x/2)# and determine the radius of convergence?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7