Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 782: 66


$$ g_{xxyz}= 360 x^2y^4z^5 .$$

Work Step by Step

Since $ g(x,y,z)=x^4y^5z^6$, then we have $$ g_x= 4x^3y^5z^6, \quad g_{xx}= 12x^2y^5z^6 .$$ Then, we have $$ g_{xxy}= 60x^2y^4z^6, \quad g_{xxyz}= 360 x^2y^4z^5 .$$
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