Find all the second order partial derivatives of the given function. f(x, y) = xye ¯y< = 0; dy2 = ey(1 - y2) 3): %3D dyðx dxdy = 2xyey22 - 6): dyðx dxdy 4 = ye'", - 2xyey"v2 - 1); dy dyðx axdy = 0; dy = 2xyey22 . 3); dyðx dxdy

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 20E
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Question 1
Find all the second order partial derivatives of the given function.
fx, y) %3 хуе "У+
= 0;
= 2xye'y²{2y² - 3);
dyðx
dxdy
= ye'y?.
- 2xye'y(2y2 - 6);
dydx
dxdy
= yey?,
2xye'y"y² - 1);
= ey(1 - y²)
=
dydx
дхду
= 0;
- 3);
dyðx dxdy
Transcribed Image Text:Question 1 Find all the second order partial derivatives of the given function. fx, y) %3 хуе "У+ = 0; = 2xye'y²{2y² - 3); dyðx dxdy = ye'y?. - 2xye'y(2y2 - 6); dydx dxdy = yey?, 2xye'y"y² - 1); = ey(1 - y²) = dydx дхду = 0; - 3); dyðx dxdy
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