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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 1-14, find the first partial derivatives. See

Z  = ln  x   +   y x     y

To determine

To calculate: The first partial derivatives for the function z=ln(x+yxy).

Explanation

Given information:

The provided function is z=ln(x+yxy).

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.

Calculation:

Consider the provided function is,

z=ln(x+yxy)

Partially derivative of the function z=ln(x+yxy) with respect to x.

zx=x(ln(x+yxy))=x(ln(x+y))x(ln(xy))=1x+y1xy=xy(x+y)(x+y)(xy)

Further solve the above equation.

zx=xyxyx2y2=2yx2y2

Partially derivative of the function z=ln(x+yxy) with respect to y

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