University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 39



Work Step by Step

$y=\frac{3}{(5x^2+\sin{2x})^{\frac{3}{2}}}=3{(5x^2+\sin{2x})^{\frac{-3}{2}}}$ on differentiating both sides: $\frac{dy}{dx}=3\frac{-3}{2}{(5x^2+\sin{2x})^{\frac{-5}{2}}}\frac{(d(5x^2+\sin{2x}))}{dx}$ $\frac{dy}{dx}=\frac{-9}{2}{(5x^2+\sin{2x})^{\frac{-5}{2}}}(10x+2\cos{2x})$
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