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 - Preliminary Questions - Page 135: 4



Work Step by Step

If $ f(x)=x^6$, then we have $$ f'(x)=6x^5, \quad f''(x)=5\times 6 x^4, \quad f'''(x)=4\times 5\times 6 x^3,$$ $$ f^{(4)}(x)=3\times 4\times 5\times 6 x^2, \quad f^{(5)}(x)=2\times 3\times 4\times 5\times 6 x $$ and finally, the sixth derivative is $ f^{(6)}(x)=1\times 2\times 3\times 4\times 5\times 6 =6!$.
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