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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 and Evaluating Partial Derivatives In Exercises 33-40, find the first partial derivatives with respect to x, y, and z, and evaluate each at the given point.

w = x y e 9 z 3 ; ( 2 , 3 , 1 3 )

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=xye9z3 at point (2,3,13).

Explanation

Given information:

The provided function is w=xye9z3 and the point is (2,3,13).

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=xye9z3

Partially derivative of the function w=xye9z3 with respect to x.

wx=x(xye9z3)=ye9z3x(x)=ye9z3(1)=ye9z3

Substitute (x,y,z)=(2,3,13) into the function wx.

wx|(2,3,13)=3e9(13)3=3e13

Partially derivative of the function w=xye9z3 with respect to y.

wy=y(xye9z3)=xe9z3y(y)=xe9z3(1)=xe9z3

Substitute (x,y,z)=(2,3,13) into the function wy.

wy|(2,3,13)=2e9(13)3=2e13

Partially derivative of the function w=xye9z3 with respect to z

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