   Chapter 7.4, Problem 45E

Chapter
Section
Textbook Problem

Finding Second Partial Derivatives In Exercises 45-52, find the four second partial derivatives. See Example 6. z = x 3 − 4 y 2

To determine

To calculate: The second partial derivatives for the function z=x34y2.

Explanation

Given information:

The provided function is z=x34y2.

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.

According to Higher-Order Partial Derivatives,

x(fx)=2fx2=fxxy(fy)=2fy2=fyyy(fx)=2fyx=fxyx(fy)=2fxy=fyx

Calculation:

Consider the provided function is,

z=x34y2

Partially derivative of the function z=x34y2 with respect to x.

zx=x(x34y2)=x(x3)4y2x(1)=3x2

Partially derivative of the function z=x34y2 with respect to y

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