   Chapter 14.4, Problem 28E

Chapter
Section
Textbook Problem

Find the differential of the function.28. T = v 1+ uvw

To determine

To find: The differential of the function T(u,v,w)=v1+uvw .

Explanation

The given function T=v1+uvw

The differential function dT is defined as, dT=Tudu+Tvdv+Twdw .

Take partial derivative with respect to u in the equation (1),

Tu=v(1)(1+uvw)11(vw)=v2w(1+uvw)2=v2w(1+uvw)2

Thus, Tu=v2w(1+uvw)2 .

Take partial derivative with respect to v in the equation (1),

Tv=1(1+uvw)v(uw)(1+uvw)2=1+uvwuvw(1+uvw)2=1(1+uvw)2

Therefore, Tv=1(1+uvw)2

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