Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.2 - The Derivative as a Function - Exercises 3.2 - Page 115: 11

Answer

$\dfrac{3}{2}q^{\frac{1}{2}}$

Work Step by Step

Use derivative formula; $f(x)= x^n \implies f'(x)= n x^{n-1}$ Consider $p(q) =q^{\frac{3}{2}}$ Now, $p'(q) =( \dfrac{3}{2})q^{(\frac{3}{2}-1)}=\dfrac{3}{2}q^{\frac{1}{2}}$
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