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Chapter 12: Q. 29 (page 944)

Find the first-order partial derivatives for the functions in Exercises 27鈥�36.

fx,y=xy

Short Answer

Expert verified

The first-order partial derivatives are 鈭�f鈭�x=yxy-1and鈭�f鈭�y=xylnx

Step by step solution

01

Given 

The given function is: fx,y=xy

02

To find  

We have to find the first-order partial derivatives.

03

Calculation  

fx,y=xy鈭�f鈭�x=鈭�鈭�xxy鈭�f鈭�x=yxy-1fx,y=xy鈭�f鈭�y=鈭�鈭�yxy鈭�f鈭�y=xylnxHence,鈭�f鈭�x=yxy-1and鈭�f鈭�y=xylnx

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Most popular questions from this chapter

Partial derivatives: Find all first- and second-order partial derivatives for the following functions:

f(x,y,z)=ln鈦�(x+y+z)

Letz=(f(x,y))n.Showthat鈭�z鈭�x=n(f(x,y))n-1鈭�f鈭�xand鈭�z鈭�y=n(f(x,y))n-1鈭�f鈭�y.

In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.

f(x,y,z)=xyzwhenx2+y2+z2=9

Describe the meanings of each of the following mathematical expressions:

鈭�f(x,y)

Sketch the level curves f(x, y) = c of the following functions for c = 鈭�3, 鈭�2, 鈭�1, 0, 1, 2, and 3:

f(x,y)=x鈭�sin鈭�1鈦�y
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