Determine whether the given function satisfies a Laplace equation.
-$$f ( x , y , z ) = \cos ( 6 x ) \sin ( - 5 y ) e ^ { ( \sqrt { 61 } z ) }$$

Question

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A function satisfies the Laplace equation if the sum of its second partial derivatives with respect to each variable equals zero. For the given function, the sum of the second partial derivatives does not equal zero.

Determine Whether the Given Function Satisfies a Laplace Equation f(x,y,z)=cos⁡(6x)sin⁡(−5y)e(61z)f ( x , y , z ) = \cos ( 6 x ) \sin ( - 5 y ) e ^ { ( \sqrt { 61 } z ) }f(x,y,z)=cos(6x)sin(−5y)e(61​z)

Determine Whether the Given Function Satisfies a Laplace Equation $f ( x , y , z ) = \cos ( 6 x ) \sin ( - 5 y ) e ^ { ( \sqrt { 61 } z ) }$