To determine Calculate the first order partial derivatives ∂ f ∂ x and ∂ f ∂ y . Explanation Given information: The function f ( x , y ) = ( 2 x − 3 y ) 3 . Calculation: Provide the function as follows. f ( x , y ) = ( 2 x − 3 y ) 3 (1) Calculate the first order partial derivative ∂ f ∂ x as shown below. Differentiate Equation (1) with respect to x . ∂ f ∂ x = ∂ ∂ x ( ( 2 x − 3 y ) 3 ) = 3 ( 2 x − 3 y ) 2 ∂ ∂ x ( 2 x − 3 y ) = 3 ( 2 x − 3 y ) 2 ( 2 ) = 6 ( 2 x − 3 y ) 2 Thus, the first order partial derivative ∂ f ∂ x = 6 ( 2 x − 3 y ) 2 _

4th Edition

ISBN: 9780134439099

Author: Hass, Joel., Heil, Christopher , WEIR, Maurice D.

Publisher: Pearson,

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter 14.3, Problem 6E

To determine

Calculate the first order partial derivatives ∂f∂x and ∂f∂y.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 5E

Chapter 14.3, Problem 7E

Students have asked these similar questions

2. A tank with a capacity of 650 gal. originally contains 200 gal of water with 100 lb. of salt in solution. Water containing 1 lb. of salt per gallon is entering at a rate of 4 gal/min, and the mixture is allowed to flow out of the tank at a rate of 3 gal/min. a. Find the amount of salt in the tank at any time prior to the instant when the tank begins to overflow (650 gallons). b. Find the concentration (in pounds per gallon) of salt in the tank when the tank hits 400 gallons. D.E. for mixture problems: dv dt=11-12 dA A(t) dt

- Suppose that you have the differential equation: dy = (y - 2) (y+3) dx a. What are the equilibrium solutions for the differential equation? b. Where is the differential equation increasing or decreasing? Show how you know. Showing them on the drawing is not enough. c. Where are the changes in concavity for the differential equation? Show how you know. Showing them on the drawing is not enough. d. Consider the slope field for the differential equation. Draw solution curves given the following initial conditions: i. y(0) = -5 ii. y(0) = -1 iii. y(0) = 2

5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I purposefully removed the units- don't worry about them. Assume no conversions are needed.) a) Find the equation for the displacement of the spring mass at time t. b) Write the equation for the displacement of the spring mass in phase-mode form. c) Characterize the damping of the spring mass system as overdamped, underdamped or critically damped. Explain how you know. D.E. for Spring Mass Systems k m* g = kLo y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo m 2 A₁ = √c₁² + C₂² Q = tan-1

Chapter 14 Solutions

Thomas' Calculus

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.