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If u, v and w are functions of x, then s...

If u, v and w are functions of x, then show that `d/(dx)(u.v.w)=(d u)/(dx)v.w+u.(d v)/(dx).w+u.v(d w)/(dx)` in two ways - first by repeated application of product rule, second by logarithmic differentiation.

Text Solution

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Using Product Rule , `(d(uvw))/dx=((d(uv))/dx)w+((d(w))/dx)uv`
`w*v*(d(u))/(dx)+w*u*(d(v))/(dx)+u*v*(d(w))/(dx)`
Now by using log,
`y=uvw`
taking log on both sides , we have
`logy=logu+logv+logw`
...
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