(a) Use the methods of Example 6 and formula (10) in this section to determine ∂2/∂x2 an...

(a) Use the methods of Example 6 and formula (10) in this section to determine ∂²/∂x² and ∂²/∂y² in terms of the polar partial differential operators (Hint: You will need to use the product rule.)

Use part (a) to show that the Laplacian operator ∂²/∂x² + ∂²/∂y² is given in polar coordinates by the formula