   Chapter 7.5, Problem 12SWU ### 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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# In Exercises 9-14, find all first and second partial derivatives. z = 2 x 2 − 3 x y + y 2

To determine

To calculate: The first and second partial derivatives of function z=2x23xy+y2.

Explanation

Given Information:

The provided function is z=2x23xy+y2.

Formula used:

The first partial derivatives of the function z=f(x,y) are zx=x[f(x,y)], zy=y[f(x,y)].

The second partial derivatives of the function z=f(x,y) are,

2fx2=x(fx)=fxx

And,

2fy2=y(fy)=fyy

Also,

2fxy=x(fy)=fyx

Also,

2fyx=y(fx)=fxy

Calculation:

Consider the function, z=2x23xy+y2

The first partial derivatives of the function are,

zx=x(2x23xy+y2)=22x31y+0=4x3y …… (1)

And

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