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( u=f(e^{y-z},e^{z-x},e^{x-y}) ext{find} dfrac{partial u}{partial x}+dfrac{partial u}{partial y}+dfrac{partial u}{partial z} )
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Answer: Let u1=eyz,u2=ezx,u3=exy. Then by chain rule,

ux=ux=uu1u1x+uu2u2x+uu3u3x

              =uu1.0uu2.ezx+uu3exy.

ux=u2uu2+u3uu3...................................(1)

Similarly,

uy=uy=uu1u1y+uu2u2y+uu3u3y.

              =uu1eyz+uu2.0uu3exy

              =u1uu1u3uu3.................................(2)

uz=uz=uu1u1z+uu2u2z+uu3u3z

              =uu1eyz+uu2ezx+uu3.0

              =u1uu1+u2uu2...............................(3)

Adding (1), (2) and (3), we get ux+uy+uz=0.              Answer.

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