48.3k views
3 votes
In verifying Clairaut’s theorem for the function u=eˣʸ sin⁡(y), what property is being checked?

a) Continuity
b) Symmetry of mixed partial derivatives
c) Differentiability
d) Stationary points analysis

User RageZ
by
8.0k points

1 Answer

4 votes

Final answer:

In verifying Clairaut’s theorem for the function u=eˣʸ sin⁡(y), we are checking the symmetry of mixed partial derivatives.

Step-by-step explanation:

Clairaut's theorem states that if the mixed partial derivatives of a function are continuous on a domain, then the order of differentiation does not matter for any point within that domain.

In the case of verifying Clairaut's theorem for the function u=eˣʸ sin⁡(y), we are checking the symmetry of mixed partial derivatives.

To verify this symmetry, we need to compute the second-order partial derivatives ∂²u/∂x∂y and ∂²u/∂y∂x.

If these partial derivatives are equal, then Clairaut's theorem holds true for the function.

User Joshlsullivan
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories