Chapter 14.3, Problem 9E

### 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

# If the joint cost function for two products is C ( x , y )= x y 2 + 1 dollars (a) find the marginal cost (function) with respect to x.(b) find the marginal cost with respect to y.

(a)

To determine

To calculate: The marginal cost with respect to x if the joint cost function for two products is given by C(x,y)=xy2+1 dollars.

Explanation

Given Information:

The joint cost function for two products is given by C(x,y)=xy2+1 dollars.

Formula used:

For a joint cost function of the form C(x,y), the marginal cost with respect to x is given by âˆ‚Câˆ‚x and the marginal cost with respect to y is given by âˆ‚Câˆ‚y.

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

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

Chain rule for the function f(x)=u(v(x)) is fâ€²(x)=uâ€²(v(x))â‹…vâ€²(x).

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

The 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)

(b)

To determine

To calculate: The marginal cost with respect to y if the joint cost function for two products is given by C(x,y)=xy2+1 dollars.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Write the sum in expanded form. 5. k=042k12k+1

Single Variable Calculus: Early Transcendentals, Volume I