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If $ u=f(x-y,y-z,z-x) , $ then show that $ \dfrac{\partial u}{\partial x} + \dfrac{\partial u}{\partial y} + \dfrac{\partial u}{\partial z} \;=\; 0 $
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written 7.9 years ago by
teamques10
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Let, p = x – y, q = y – z and r = z – x. ∴ u =f(p, q, r)
$ \therefore \dfrac{\partial p}{\partial x}=1 \; \; and \; \; \dfrac{\partial p}{\partial y}=-1 $
Similarly,
$ \dfrac{\partial q}{\partial y}=1 \; , \; \dfrac{\partial q}{\partial z}=-1 \; , \; …
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