Explanation Given: The function is f ( x , y ) = 2 x + 5 y 2 3 x 2 + y 2 ... ( 1 ) . Approach: The partial derivative of f with respect to y is the derivative of f obtained by treating x as a constant and y as a variable, while the partial derivative of f with respect to x is the derivative of f obtained by treating x as a variable and y as a constant. Calculation: Take partial derivative of f with respect to x in the equation ( 1 ) , f x ( x , y ) = 2 ( 3 x 2 + y 2 ) − 6 x ( 2 x + 5 y 2 ) ( 3 x 2 + y 2 ) 2 = 6 x 2 + 2 y 2 − 12 x 2 − 30 x y 2 ( 3 x 2 + y 2 ) 2 = − 6 x 2 + 2 y 2 − 30 x y 2 ( 3 x 2 + y 2 ) 2 Take partial derivative of f with respect to y in the equation ( 1 ) ,

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

See similar textbooks

Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Videos

Question

Chapter 9.CR, Problem 30CR

To determine

To find:

The value of fx(x,y) and fy(x,y) for the function f(x,y)=2x+5y23x2+y2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.CR, Problem 29CR

Chapter 9.CR, Problem 31CR

Students have asked these similar questions

Evaluate the next integral

1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative maximum and minimum values of f. (a) f(x) = x² - 2x²+3 (b) f(x) = (x+1)5-5x-2 (c) f(x) = x2 x-9 2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f. (a) f(x) = x - 2x²+3 (b) g(x) = x³- x (c) f(x)=x-6x3 + x-8 3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test. (a) f(x)=1+3x² - 2x3 (b) g(x) = 2x3 + 3x² - 12x-4

Find the Soultion to the following dy differential equation using Fourier in transforms: = , хуо, ухо according to the terms: lim u(x,y) = 0 x18 lim 4x (x,y) = 0 x14 2 u (x, 0) = =\u(o,y) = -y لو

Chapter 9 Solutions

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The value of f x ( x , y ) and f y ( x , y ) for the function f ( x , y ) = 2 x + 5 y 2 3 x 2 + y 2 .

Solution Summary: The author explains the function f(x,y)=2x+5y

Concept explainers

Videos

To find:

The value of fx(x,y) and fy(x,y) for the function f(x,y)=2x+5y23x2+y2.

Want to see the full answer?

Chapter 9 Solutions

The value of f x ( x , y ) and f y ( x , y ) for the function f ( x , y ) = 2 x + 5 y 2 3 x 2 + y 2 .

Solution Summary: The author explains the function f(x,y)=2x+5y

Concept explainers

Videos

To find: The value of fx(x,y) and fy(x,y) for the function f(x,y)=2x+5y23x2+y2.

Want to see the full answer?

Chapter 9 Solutions

To find:

The value of fx(x,y) and fy(x,y) for the function f(x,y)=2x+5y23x2+y2.