Find the second order derivatives of the function

e^6x cos 3x

Let us take y = e^6x cos 3x

Now,

= 6e^6xcos3x - 3e^6xsin3x

= 36e^6xcos3x – 18e^6xsin3x -3[sin3x.e^6x.6 + e^6x.cos3x.3]

= 36e^6xcos3x – 18e^6xsin3x – 18e^6xsin3x -9e^6xcos3x

= 27e^6xcos3x -36e^6xsin3x

= 9e^6x(3cos3x – 4sin3x)