Aspire Faculty ID #17069 · Topic: AMU MCA 2021 · Just now
AMU MCA 2021

If $x + y + z = u$ $y + z = uv$ $z = uvw$ then the value of the Jacobian $\dfrac{\partial(x,y,z)}{\partial(u,v,w)}$ is

Solution

Given $z = uvw$ $y + z = uv$ $\Rightarrow y = uv - uvw = uv(1 - w)$ Now $x + y + z = u$ $\Rightarrow x = u - y - z$ Substitute: $x = u - uv(1 - w) - uvw$ $x = u - uv + uvw - uvw$ $x = u - uv$ $x = u(1 - v)$ So, $x = u(1 - v)$ $y = uv(1 - w)$ $z = uvw$
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