# True-False Quiz Question 13: Determining Derivatives via Coefficients of a Power Series

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• Published on Jan 25, 2024

In this video I show that we can solve for any given derivative of a function just by looking at its coefficients if it can be written as a convergent power series. The coefficients of a power series are given by the formula: (n-th derivative at a) / n!. In our question, we are asked to solve for the 3rd derivative of such a function. I show that we can solve it via the coefficients of a power series, and then confirm our result by solving for the derivatives directly. Thus, the answer to the question is True.

Time stamps:

• Question 13: 0:00
• Solution 1: True. Coefficients of a Power Series: 0:27
• n=3 coefficient: 3:15
• Solution 2: Differentiating f(x) directly: 4:32
• Third derivative is 2: 6:27

Full video below:

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