Chapter 14, Problem 7RE

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# In Problems 7-12, find z x  and  z y . 7.   z = 4 x 2 y 3 + x y

To determine

To calculate: The partial derivatives zx and zy of the function z=4x2y3+xy.

Explanation

Given Information:

The provided function is z=4x2y3+xy.

Formula used:

For a function z(x,y), the partial derivative of z with respect to x is calculated by taking the derivative of z(x,y) with respect to x and keeping the other variable y constant. The partial derivative of z with respect to x is denoted by zx and the partial derivative of z with respect to y is denoted by zy.

Power of x rule for a real number n is such that, if f(x)=xn then fâ€²(x)=nxnâˆ’1.

Quotient rule for function f(x)=u(x)v(x), where u and v are differentiable functions of x, then fâ€²(x)=v(x)â‹…uâ€²(x)âˆ’u(x)â‹…vâ€²(x)(v(x))2.

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Calculation:

Consider the provided function, z=4x2y3+xy

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