Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - Review Exercises: 47

Answer

$f''(x) = (\frac{225}{4})\sqrt x$

Work Step by Step

1. Find $f'(x)$ $f(x) = 15x^{\frac{5}{2}}$ $f'(x) = (15 \times \frac{5}{2})x^{(\frac{5}{2} - 1)}$ $f'(x) = (\frac{75}{2})x^{(\frac{3}{2})}$ 2. Find $f''(x)$ $f'(x) = (\frac{75}{2})x^{(\frac{3}{2})}$ $f''(x) = (\frac{75}{2} \times \frac{3}{2})x^{(\frac{3}{2}- 1)}$ $f''(x) = (\frac{225}{4})x^{\frac{1}{2}}$ $f''(x) = (\frac{225}{4})\sqrt x$
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