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Andresfon12
 2 years ago
Best ResponseYou've already chosen the best response.0\[a) \frac{ z }{ y } (1, 1/2) if z= e^{x+2y} \sin y\] b) fx (pi/3, 1) if f(x, y) = x ln (y cos x)

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0a) I don't understand, maybe something went wrong with typing in the formula? b) You need fx, so consider y as a constant. e'll need the Product Rule here, and also the Chain Rule...

Andresfon12
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1361122439795:dw

Andresfon12
 2 years ago
Best ResponseYou've already chosen the best response.0fx = 1/ (cos x)* sin (x)

muhammad9t5
 2 years ago
Best ResponseYou've already chosen the best response.0take ln on both sides.

Andresfon12
 2 years ago
Best ResponseYou've already chosen the best response.0@muhammad9t ibyt i think i already did that for part b

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0I understand what you wrote in a) now ;) \[\frac{ \delta z }{ \delta y }=2e^{x+2y}\sin y+e^{x+2y} \cos y=e^{x+2y}(2\sin y + \cos y)\]Now set x = 1 and y = ½: \[\frac{ \delta z }{ \delta y }(1,\frac{ 1 }{ 2 })=e^{2}(2\sin 1+\cos \frac{ 1 }{ 2 })\]

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0Second one: f(x, y) = x ln(ycos x). I need fx, so y is constant:\[\frac{ \delta f }{ \delta x }=1 \cdot \ln(y \cos x)+x \cdot \frac{ 1 }{ y \cos x }\cdot y \sin x=\ln(y \cos x) x \tan x\]Now set x = pi/3, y = 1:\[\ln(\cos \frac{ \pi }{ 3 })\frac{ \pi }{ 3 }\tan \frac{ \pi }{ 3 }=\ln \frac{ 1 }{ 2 }\frac{ \pi }{ 3 }\sqrt{3}=(\ln2+\frac{ \pi }{ 3 }\sqrt{3})\]
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