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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7.5, Problem 23QY
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Problem 21QY
Problem 22QY
Problem 23QY
Problem 24QY
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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In Exercises 20-23, find the first partial derivatives and evaluate each at the point (-2, 3).

f ( x , y ) = ln ( 2 x + 7 y )

To determine

To calculate: The first order partial derivative of the function f(x)=ln(2x+7y) with respect to x and y respectively and find the value of that partial derivative at point (−2,3).

Explanation

Given Information:

The provided function is f(x)=ln(2x+7y) and the provided point is (−2,3).

Formula used:

If the function f(x,y) is of the form ln(u+v), the partial derivative of first order with respect

to x,

fx(x,y)=1u+vux

And the partial derivative of that function with respect to y,

fy(x,y)=1u+vuy

Where u,v are the function of x and function of y respectively

u=u(x)v=v(y)

Step 1: Write the given function.

Step 2: Find the partial derivative of first order with respect to x with the help of fx(x,y)=1u+vux formula.

Step 3: Find the partial derivative of first order with respect to y with the help of fy(x,y)=1u+vuy formula.

Step 4: Replace x by 2 and y by 3 in the equation fx(x,y).

Step 5: Replace x by 2 and y by 3 in the equation fy(x,y).

Calculation:

Consider the given equation,

f(x,y)=ln(2x+7y)

So, the equation of partial derivative of the function f(x,y) of first order with respect to x with the help of fx(x,y)=1u+vux formula

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 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11.If

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In Exercises 1 to 20, let U = {1, 2, 3, 4, 5, 6, 7, 8}, A= {2, 4,6}, B = {1, 2,5,8}, and C = {1, 3, 7}. Find ea...

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