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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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Find the first partial derivatives of w = x 2 y ln ( x z ) with respect to x, y, and z.

In Example 5, the Product Rule is used only when finding the partial derivative with respect to x. For

w y and w z x is considered to be constant, so the Constant Multiple Rule is used.

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=x2yln(xz).

Explanation

Given information:

The provided function is w=x2yln(xz).

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,

w=x2yln(xz)

Partially derivative of the function w=x2yln(xz) with respect to x.

wx=x(x2yln(xz))=yln(xz)x(x2)+x2yx(ln(xz))=2xyln(xz)+x2y1xzzx(x)=xy(2ln(xz)+1)

Partially derivative of the function w=x2yln(xz) with respect to y

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