and yyzEl zzy∂=⋅∂xxzEl zzx∂=⋅∂11.8 Partial elasticities()'()()xxEl f xfxf x=⋅⋅If fis differentiable in xand f(x) ≠01. Function of one variable:2. Function of 2 variables:xxzEl zzx∂=⋅=⋅=⋅=⋅∂(),0af xAxx=>=>==1()axaxEl f xAaxAx-=⋅⋅a=();,0abf xAx yx y=>1by aabxAaxAx y-=⋅a=11.2 Higher-order partial derivativesFind the second-order partial derivatives of the following function: 22()ffxdx dx∂∂∂∂∂∂∂∂=∂22(21)2xyyx∂=+=∂223( ,)f x yx yxy=++=+2()ffy xy dx∂∂∂∂∂=∂∂∂∂∂2(21)xyy∂=+∂4xy=2()ffx ydx dy∂∂∂=∂ ∂∂ ∂22(23)x yyx∂=+∂4xy=22()ffydy dy∂∂∂∂∂∂∂∂=∂22(23)x yyy∂=++∂226xy=+=+==11.1 Higher-order partial derivativesYou can also use the following notation:For most functions these two ‘mixed’ second-order partial derivatives (or ‘cross-partials) are equal.12''( ,)fx y21'' (,)fx y11.1 Example 5b/page 380Determine the domain of the function given by the following formula and draw the set in the xy-plane.22222( ,)9()4g x yxyxy=+-+=+-++++-+-22Domain: 49xy<+≤≤222is the graph consisting all the points on the circle with centre at the origin and radius .xyrr+=+
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411.1 Example22222( ,)9()4g x yxyxy=+-+++--22Domain: 49xy<+≤≤6.11 ExampleFind the domain and compute the derivative:yis defined for
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