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In this video I prove that the derivatives of a Taylor Polynomial are equal to the derivatives of the corresponding function used in the approximation when x = a. This is because any derivative at x = a of any Taylor polynomial cancels out all the terms (since a - a = 0) except the first term, which is just the corresponding derivative of f at x = a.
Timestamps:
Exercise 1: Taylor Derivatives are the same as the function used in the Taylor Polynomial: 0:00
Solution: Taylor derivatives cancel out all the terms except the first: 0:30
n-th Taylor derivative is equal to the n-th derivative of f: 8:09
Exercise 1: Taylor Derivatives Equal the Function's Derivatives at x = a