Expert: Paul Klarreich - 4/2/2008

Question
How are all the second-order partial derivatives of the function z = 9xln(8x^3y)worked out? Thank you.

Answer
Questioner:   James
Category:  Calculus
Private:  No
 
Subject:  second-order partial derivatives
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Hi, James,

Question:  How are all the second-order partial derivatives of the function
z = 9xln(8x^3y)worked out?

There are four:

z[x,x] : differentiate w.r.t. x, then differentiate w.r.t. x (again)

z[y,y] : differentiate w.r.t. y, then differentiate w.r.t. y (again)

z[x,y] : differentiate w.r.t. x, then differentiate w.r.t. y

z[y,x] : differentiate w.r.t. y, then differentiate w.r.t. x

As a check, the last two should be the same. When you diff w.r.t. x, you treat y as a constant and vice versa.