   Chapter 7.5, Problem 21QY ### 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
1 views

# In Exercises 20-23, find the first partial derivatives and evaluate each at the point ( − 2 ,   3 ) . f ( x , y ) = 3 x − y 2 x + y

To determine

To calculate: The first partial derivatives for the function f(x,y)=3xy2x+y and their values at point (2,3).

Explanation

Given Information:

The provided function is f(x,y)=3xy2x+y and the point is (2,3).

Formula used:

If the function is f(x,y)=u(x,y)v(x,y),

Then, the first order partial derivative of f(x,y) with respect to x is,

fx(x,y)=v(x,y)ux(x,y)u(x,y)vx(x,y)[v(x,y)]2

The first order partial derivative of f(x,y) with respect to y is,

fy(x,y)=v(x,y)uy(x,y)u(x,y)vy(x,y)[v(x,y)]2

Calculation:

Consider the function,

f(x,y)=3xy2x+y

The first partial derivatives are,

fx=(x+y)(310)(3xy2)(1+0)(x+y)2=3x+3y3x+y2(x+y)2=y2+3y(x+y)2=y(3+y)(x+y)2

And,

fy(x,y)=(x+y)(02y)(3x

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Expand each expression in Exercises 122. (2xy)y

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Find limh01h22+h1+t3dt

Single Variable Calculus: Early Transcendentals, Volume I

#### The area of the shaded region is given by:

Study Guide for Stewart's Multivariable Calculus, 8th

#### The graph at the right has a local maximum at x ______. a) 1, 3, and 5 b) 2 c) 4 d) 2 and 4

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 