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Question
If w(x, y) = xy + sin(xy), then Prove that `(del^2w)/(delydelx) = (del^2w)/(delxdely)`
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Solution
w(x, y) = xy + sin(xy)
L.H.S = `(del^2w)/(delydelx)`
= `del/(dely) [(delw)/(delx)]`
= `del/(dely) [y + y cos (xy)]`
= `1 + y[ x sin (xy)]`
= `1 - xy sin (xy)` .......(1)
R.H.S =`(del^2w)/(delxdely)`
= `del/(delx) [(delw)/(dely)]`
From (1) and (2)
⇒ `(del^2w)/(delydelx) = (del^2w)/(delxdely)`
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