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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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In Exercises 7-10, find the first partial derivatives.

f ( x , y , z ) = x ( x 2 + 3 y 2 z 2 )

To determine

To calculate: The first partial derivatives of the function f(x,y,z)=x(x2+3y2z2).

Explanation

Given Information:

The provided function is f(x,y,z)=x(x2+3y2z2).

Formula used:

The first partial derivatives of the function w=f(x,y,z) are,

wx=x[f(x,y,z)]wx=fx(x,y,z)

And,

wy=y[f(x,y,z)]wy=fy(x,y,z)

Also,

wz=z[f(x,y,z)]wz=fz(x,y,z)

Calculation:

Consider the function, f(x,y,z)=x(x2+3y2z2)

Simplify the function,

f(x,y,z)=x3+3xy2xz2

The first partial derivatives of the function are,

x[f(x<

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