Mclaurin Series

[lofty mulch]

How do I prove the nth derivative of the function is always 0 at x=0? Also, how is the Maclaurin series for this function 0, when it is only 0 at x=0?

[sharp ravine]

Found this for the first part

https://www.reddit.com/r/learnmath/comments/ib0w7e/show_that_the_nth_derivative_of_a_function_at_0/?utm_source=share&utm_medium=android_app&utm_name=androidcss&utm_term=1&utm_content=share_button

Basically the same question

,w Maclaurin series e^{-1/x^2}