Answer
$-\frac{(5p^2+2p)^{5/2}}{15p+3}$
Work Step by Step
Given $q=(5p^2+2p)^{-3/2}$, we have $dq=-\frac{3}{2}(5p^2+2p)^{-5/2}(10pdp+2dp)=-3(5p^2+2p)^{-5/2}(5p+1)dp$
Thus
$\frac{dp}{dq}=-\frac{(5p^2+2p)^{5/2}}{15p+3}$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 3: Derivatives - Practice Exercises - Page 178: 50
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