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Andresfon12 Group TitleBest 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)
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.0
a) 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...
 one year ago

Andresfon12 Group TitleBest ResponseYou've already chosen the best response.0
dw:1361122439795:dw
 one year ago

Andresfon12 Group TitleBest ResponseYou've already chosen the best response.0
fx = 1/ (cos x)* sin (x)
 one year ago

muhammad9t5 Group TitleBest ResponseYou've already chosen the best response.0
take ln on both sides.
 one year ago

Andresfon12 Group TitleBest ResponseYou've already chosen the best response.0
@muhammad9t ibyt i think i already did that for part b
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.0
I 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: \[\frac{ \delta z }{ \delta y }(1,\frac{ 1 }{ 2 })=e^{2}(2\sin 1+\cos \frac{ 1 }{ 2 })\]
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.0
Second 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:\[\ln(\cos \frac{ \pi }{ 3 })\frac{ \pi }{ 3 }\tan \frac{ \pi }{ 3 }=\ln \frac{ 1 }{ 2 }\frac{ \pi }{ 3 }\sqrt{3}=(\ln2+\frac{ \pi }{ 3 }\sqrt{3})\]
 one year ago
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