Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 12 - Functions of Several Veriables - 12.4 Partial Derivatives - 12.4 Exercises - Page 904: 2

Answer

$${f_x}\left( {x,y} \right) = 6xy + {y^3}{\text{ and }}{f_y}\left( {x,y} \right) = 3{x^2} + 3x{y^2}$$

Work Step by Step

$$\eqalign{ & {\text{Let }}f\left( {x,y} \right) = 3{x^2}y + x{y^3} \cr & {\text{Calculate }}{f_x}\left( {x,y} \right) \cr & {f_x}\left( {x,y} \right) = \frac{\partial }{{\partial x}}\left[ {3{x^2}y + x{y^3}} \right] \cr & {f_x}\left( {x,y} \right) = 6xy + {y^3} \cr & \cr & {\text{Calculate }}{f_y}\left( {x,y} \right) \cr & {f_y}\left( {x,y} \right) = \frac{\partial }{{\partial y}}\left[ {3{x^2}y + x{y^3}} \right] \cr & {f_y}\left( {x,y} \right) = 3{x^2} + 3x{y^2} \cr & \cr & {f_x}\left( {x,y} \right) = 6xy + {y^3}{\text{ and }}{f_y}\left( {x,y} \right) = 3{x^2} + 3x{y^2} \cr} $$
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