Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 9 - Multiveriable Calculus - 9.2 Partial Derivatives - 9.2 Exercises - Page 478: 3


$$f_x(x,y) =-4y ,\ \ f_y(x,y) =-4x+18y^2 , \ \ f_x(2,-1) =4\ f_y(-4,3) =178$$

Work Step by Step

Given $$f(x, y)=-4 x y+6 y^{3}+5$$ Since \begin{align*} f_x(x,y)&=\frac{\partial f }{\partial x}\left(-4 x y+6 y^{3}+5\right)\\ &=-4y \end{align*} \begin{align*} f_y(x,y)&=\frac{\partial f }{\partial y}\left(-4 x y+6 y^{3}+5\right)\\ &=-4x+18y^2 \end{align*} and \begin{align*} f_x(2,-1) &=4\\ f_y(-4,3)&=178 \end{align*}
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