Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.4 Tangent Planes and Linear Approximations - 14.4 Exercises - Page 975: 27



Work Step by Step

Write the differential form such as: $dw=\dfrac{\partial w}{\partial x} \times dx + \dfrac{\partial w}{\partial y} \times dy $ Write the partial derivatives with respect to $p$ and $q$. $dm= \dfrac{\partial m}{\partial p} \times dp+\dfrac{\partial m}{\partial q} \times dq$ $ \dfrac{\partial m}{\partial p} \times dp=(5) \times p^{4} \times q^{3}dp$ ....(1) and $\dfrac{\partial m}{\partial q} \times dq=(3) p^{5}q^{2}dq$ ...(2) From the equations (1) and (2) $dm=5p^{4}q^{3}dp+3p^{5}q^{2}dq$
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