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If u=xyz, v=x2+y2+x2, w=x+y+z then prove that \[ \dfrac {\partial x}{\partial u} = \dfrac {1}{(x-y)(x-z)} \]
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teamques10
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$\Large{ We \; have \\ f_1 : u-xyz = 0 , \\ f_2 : v-x^2-y^2-z^2=0, \\ f_3: w-x-y-z=0 \\ \therefore {\delta x \over \delta u }= - \bigg[ { \delta (f_1,f_2,f_3) \over \delta(u,y,z)} \bigg/ \; {\delta(f_1,f_2,f_3) \over \delta (x,y,z)} \bigg] \\ Now, \; \; { \delta (f_1,f_2,f_3) \over \delta(u,y,z)} \; …
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