Explanation Proof: The given function is, f ( x , y ) = x e y . Take partial derivative of the given function with respect to x and obtain f x . ∂ f ∂ x = ∂ ∂ x ( x e y ) = e y ∂ ∂ x ( x ) = e y ( 1 ) Hence, ∂ f ∂ x = e y (1) Take partial derivative of equation (1) with respect to y and obtain f x y . ∂ 2 f ∂ x ∂ y = ∂ ∂ y ( f x ) = ∂ ∂ y ( e y ) = e y Hence, f x y = e y . Take partial derivative of the given function with respect to y and obtain u y

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Question

Chapter 12.4, Problem 40E

To determine

To verify: The equality fxy=fyx for the function f(x,y)=xey .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.4, Problem 39E

Chapter 12.4, Problem 41E

Students have asked these similar questions

Solve this

What are the correct answers for the second and third question on this page. I am on the Cartesian vectors unit in calculu

Trolley of the overhead crane moves along the bridge rail. The trolley position is measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the forward direction. CONTROL PANEL END TRUCK- RUNWAY BEAM- BRIDGE RAIL HOIST -TROLLEY TROLLEY BUMPER TROLLEY DRIVE LPENDANT TRACK -TROLLEY CONDUCTOR TRACK WIRE ROPE -HOOK BLOCK -BRIDGE DRIVE -END TRUCK BUMPER -RUNWAY RAIL TROLLEY END STOP -CONDUCTOR BAR PENDANT FESTOONING TROLLEY FESTOONING PENDANT CABLE PENDANT x(t)=0.5t^3-6t^2+19.5t-14 v(t)=1.5t^2-12t+19.5 a(t)=(dv(t))/dt=3t-12 Fig. T2.2: The overhead crane Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20 kg, and 150 kg. Damping coefficient, D, is 40 kg/s. What is the total amount of energy required from the trolley motor to move the system [Hint: Use Newton's 2nd law to obtain the…

Chapter 12 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 12.1 - Give two pieces of information which, taken...Ch. 12.1 - Find a vector normal to the plane 2x 3y + 4z =...Ch. 12.1 - Where does the plane 2x 3y + 4z = 12 intersect...Ch. 12.1 - Give an equation of the plane with a normal vector...Ch. 12.1 - To which coordinate axes are the following...Ch. 12.1 - Describe the graph of x = z2 in 3.Ch. 12.1 - What is a trace of a surface?Ch. 12.1 - What is the name of the surface defined by the...Ch. 12.1 - What is the name of the surface defined by the...Ch. 12.1 - What is the name of the surface defined by the...

Knowledge Booster

To verify: The equality f x y = f y x for the function f ( x , y ) = x e y .

Solution Summary: The author explains how to verify the equality of the function f(x,y)=xey.

To verify: The equality fxy=fyx for the function f(x,y)=xey .

Want to see the full answer?

Chapter 12 Solutions