Question: a function fxy is called harmonic is it fulfills the...

A function f(x,y) is called harmonic is it fulfills the laplace equation.

a) Show by using the chain rule that

if

where a and b are constants.
b) Use a) to show that the function e^(2x+3y) *sin(3x-2y) is harmonic.
c)Show that the product of two harmonic functions is harmonic if their gradients is perpendicular to each other at each point.

Please explain thoroughly. :)
Thank you in advance. :)