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Homework Statement
Find the Laplacian of F = [tex]sin(k_x x)sin(k_y y)sin(k_z z)[/tex]
Homework Equations
[tex]\nabla^2 f = \left( \frac{\partial}{\partial x} +\frac{\partial}{\partial y} + \frac{\partial}{\partial z} \right) \cdot \left( \frac{\partial}{\partial x} + \frac{\partial}{\partial y} + \frac{\partial}{\partial z} \right) \cdot F[/tex]
Where F is a scalar function
The Attempt at a Solution
Biggest problem is with partial derivatives. I don't know how to approach taking a partial derivative of such a big multivariate product :( Just got the derivative of sin(x) is cos(x) and the second derivative -sin(x)
Just want to makes sure, but [tex]\frac{\partial}{\partial x}y = 0 [/tex] but [tex]\frac{\partial}{\partial x}xy = y [/tex] ?