Find the second order derivatives of the function

e6x cos 3x


Let us take y = e6x cos 3x


Now,





= 6e6xcos3x - 3e6xsin3x





= 36e6xcos3x – 18e6xsin3x -3[sin3x.e6x.6 + e6x.cos3x.3]


= 36e6xcos3x – 18e6xsin3x – 18e6xsin3x -9e6xcos3x


= 27e6xcos3x -36e6xsin3x


= 9e6x(3cos3x – 4sin3x)


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