   Chapter 7.5, Problem 23QY ### 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 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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