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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Partial Derivatives In Exercises 41-50, find the first partial derivatives.

f ( x , y ) = ln ( 5 x + 4 y )

To determine

To calculate: The partial derivative of function f(x,y)=ln(5x+4y).

Explanation

Given Information:

The provided function is f(x,y)=ln(5x+4y).

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

The differentiation of logarithmic function with respect to x by holding y constant,

x[lnf(x,y)]=1f(x,y)xf(x,y)

The differentiation of logarithmic function with respect to y by holding x constant,

y[lnf(x,y)]=1f(x,y)yf(x,y)

Calculation:

Consider the function,

f(x,y)=ln(5x+4y)

Differentiate with respect to x by holding y constant,

xf(x,y)=xln(5x+4y)

Now apply, the differentiation of logarithmic function with respect to x by holding y constant,

xln(5x+4y)=x

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