   Chapter 7.4, Problem 32E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Partial Derivatives In Exercises 29-32, find the first partial derivatives with respect to x ,   y , and  z . See Example 5. w   =   x y x   +   y  +  z

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=xyx+y+z.

Explanation

Given information:

The provided function is w=xyx+y+z.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided function is,

w=xyx+y+z

Partially derivative of the function w=xyx+y+z with respect to x.

wx=x(xyx+y+z)=(x+y+z)x(xy)(xy)x(x+y+z)(x+y+z)2=(x+y+z)(y)(xy)(1)(x+y+z)2=xy+y2+zyxy(x+y+z)2

Further solve the above equation.

wx=y2+zy(x+y+z)2

Partially derivative of the function w=xyx+y+z with respect to y.

wy=y(xyx+y+z)=(x+y+z)y(xy)(xy)y(x+y+z)(x+y+z)2=(x+y+z)(x)(xy)(1)(x+y+z)2=x2+xy+xzxy(x+y+z)2

Further solve the above equation

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