anonymous
  • anonymous
how is f x y = (-y sin xy)(x) = -xy sin xy ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
how to solve this second order partial derivative? when function f(x,y) =Sin xy.....??? i have differentiated w.r.t. x and got \[-y ^{2} Sin xy\] but to find 2nd order part. derv. i have differentiated this w.r.t. y and i have got \[-xy Sin xy -\cos xy\] is this correct?
anonymous
  • anonymous
is it?
anonymous
  • anonymous
When you take a partial w.r.t. x you hold y as a constant, so: \[D_x=-ysin(xy)-xy^2\cos(xy)\]

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anonymous
  • anonymous
plz hold on..i'll type how i had solved...
anonymous
  • anonymous
function is 'Sin xy' part.derv. wrt x=y cos xy -------eq. 1 part.derv. of eq .1 wrt x= \[-y ^{2} \sin xy\] and part.derv of eq 1 wrt y is = \[-xy \sin xy-\cos xy \] (using uv rule)
anonymous
  • anonymous
is the part.derv. of eq 1 wrt y correct?
anonymous
  • anonymous
to find part.derv. of eq 1 wrt 'y' :- \[u= y \cos xy & v=\cos xy\] then, \[{y(- \sin xy)x}-{\cos xy .1}\] and thats how i got −xysinxy−cosxy
anonymous
  • anonymous
u=y and v=cos xy
anonymous
  • anonymous
are you getting the same answer?
anonymous
  • anonymous
u der?
anonymous
  • anonymous
I thought your function was -xysin(xy)......? your partial w.r.t. x is correct what are you trying to find out ? \[f_x(x,y), f_y(x,y), or, f_{xy}(x,y)\]
anonymous
  • anonymous
the actual function is f(x,y)=Sin xy \[f_{x} (x,y)= y Cos xy \] , \[f _{xx}= - y ^{2} Sin xy \] and \[f _{xy}(x,y)= -xy Sin xy+\cos xy\]
anonymous
  • anonymous
is this correct???
anonymous
  • anonymous
Yes, thats correct
anonymous
  • anonymous
yeah i got the answer
anonymous
  • anonymous
yeah i got the answer
anonymous
  • anonymous
cool

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