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: 57


$$\frac{\partial^2 f}{\partial x^2}=6 y,\quad \frac{\partial^2 f}{\partial y^2}= -72xy^2.$$

Work Step by Step

Since $ f(x,y)=3x^2y-6xy^4$, then we have $$\frac{\partial f}{\partial x}=6xy-6y^4,\quad \frac{\partial f}{\partial y}=3x^2 -24xy^3.$$ Hence, we get $$\frac{\partial^2 f}{\partial x^2}=6 y,\quad \frac{\partial^2 f}{\partial y^2}= -72xy^2.$$
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