Q. 184.4( 45 Votes )

If u, v and w are functions of x, then show that



in two ways – first by repeated application of product rule, second by logarithmic differentiation.

Answer :

To prove:

Let y=u.v.w=u.(v.w)


(a) by applying product rule differentiate both sides with respect to x





(b) Taking log on both sides, we get


as, y=u.v.w


log y = log (u.v.w)


log y = log u + log v + log w


Now, differentiate both sides with respect to x







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