   Chapter 14.3, Problem 68E

Chapter
Section
Textbook Problem

Find the indicated partial derivative(s).68. V = ln(r + s2 + t3); ∂ 3 V ∂ r   ∂ s   ∂ t

To determine

To find: The derivative 3Vrst of the function V=ln(r+s2+t3) .

Explanation

The given function is, V=ln(r+s2+t3) .

Take the partial derivative of the given function with respect to t and obtain Vt .

Vt=t(ln(r+s2+t3))=t(ln(r+s2+t3))t(r+s2+t3)=1r+s2+t3(0+0+3t2)=3t2r+s2+t3

Thus, Vt=3t2r+s2+t3 (1)

Take the partial derivative of the equation (1) with respect to s and obtain, 2Vst .

2Vst=s(3t2r+s2+t3)=3t2s(1r+s2+t3)=3t2[(1)(r+s2+t3)2(2s)]=6st2(r+s2+t3

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