Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 136: 31


$$ f^{(n)}(x)=(-1)^n (n+1)! \ x^{-(n+2)}.$$

Work Step by Step

Since $ f(x)=x^{-2}$, then we have $$ f'(x)=(-2)x^{-3},\quad f''(x)=(-2)(-3)x^{-4}, \quad f'''(x)=(-2)(-3)(-4)x^{-5}, \cdots,$$ Hence, we get the general formula for $ f^{(n)}(x)$ as follows $$ f^{(n)}(x)=(-1)^n (n+1)! \ x^{-(n+2)}.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.