   Chapter 7.4, Problem 21E ### 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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# Finding and Evaluating Partial Derivatives In Exercises 17-24, find the first partial derivatives and evaluate each at the given point. See Example 2. f ( x ,   y )   =  ln  ( 3 x   +   5 y ) ;   ( 1 ,   0 )

To determine

To calculate: The first partial derivatives of the function f(x,y)=ln(3x+5y) at the point (1,0).

Explanation

Given information:

The provided function is f(x,y)=ln(3x+5y) and the point is (1,0).

Formula used:

The first partial derivatives of z=f(x,y) are represented as,

zx=fx(x,y)=zx=x[fx(x,y)]zy=fy(x,y)=zy=y[fy(x,y)]

The value of first partial derivatives at point (a,b) are represented as,

zx|(a,b)=fx(a,b)zy|(a,b)=fy(a,b)

Calculation:

Consider the provided function is,

f(x,y)=3exy

Partially derivative of the function f(x,y)=ln(3x+5y) with respect to x.

zx=fx(x,y)=x(ln(3x+5y))=13x+5y3=33x+5y

Substitute (x,y)=(1,0) in derivative fx(x,y)

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