   Chapter 14, Problem 16RE Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In Problems 15-18, find the second partials. ( a ) z x x     ( b ) z y y         ( c )   z x y                 ( d )   z y x 16.   z = 3 x 3 y 4 − x 2 y 2

(a)

To determine

To calculate: The second partial derivative zxx of the function z=3x3y4x2y2.

Explanation

Given Information:

The provided function is z=3x3y4x2y2.

Formula used:

For a function z(x,y), the second partial derivative,

When both derivatives are taken with respect to x is zxx=2zx2=x(zx).

When both derivatives are taken with respect to y is zyy=2zy2=y(zy).

When first derivative is taken with respect to x and second derivative is taken with respect to y is zxy=2zyx=y(zx).

When first derivative is taken with respect to y and second derivative is taken with respect to x is zyx=2zxy=x(zy).

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x)

(b)

To determine

To calculate: The second partial derivative zyy of the function z=3x3y4x2y2.

(c)

To determine

To calculate: The second partial derivative zxy of the function z=3x3y4x2y2.

(d)

To determine

To calculate: The second partial derivative zyx of the function z=3x3y4x2y2.

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