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Question

If u=sin3xcos4y then, verify 2uxy=2uyx

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Solution

ux=cos4ycos3x.3=3cos3xcos4;
uy=sin3x(sin4y)=4sin3xsin4y;
2uxy=x(uy)=u(4sin3xsin4y)
=4sin4y(cos3x.3)=12cos3xsin4y .... (1)
2uyx=y(ux)=y(3cos3xcos4y)
=3cos3x(sin4y.4)=12cos3xsin4y .... (2)
From (1) and (2), we have
2uxy=2uyx

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