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# 7。e® cos 3x

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Solution

## The given function is e 6x cos3x. Let y= e 6x cos3x. Differentiate function y with respect to x. dy dx = d( e 6x cos3x ) dx dy dx = d( e 6x ) dx .cos3x+ d( cos3x ) dx . e 6x dy dx =6 e 6x ( cos3x )−sin3x( 3 e 6x ) dy dx =3 e 6x ( 2cos3x−sin3x ) Again, differentiate with respect to x. d dx ( dy dx )= d( 3 e 6x ( 2cos3x−sin3x ) ) dx d 2 y d x 2 =3( d( e 6x ) dx ( 2cos3x−sin3x )+ d( 2cos3x−sin3x ) dx . e 6x ) d 2 y d x 2 =3( 6 e 6x ( 2cos3x−sin3x )−3( 2sin3x+cos3x ). e 6x ) d 2 y d x 2 =3( 12 e 6x cos3x−6 e 6x sin3x−6 e 6x sin3x−3 e 6x cos3x ) Simplify further, d 2 y d x 2 =3( 9 e 6x cos3x−12 e 6x sin3x ) d 2 y d x 2 =9 e 6x ( 3cos3x−4sin3x ) Thus, the second order derivative of the given function is 9 e 6x ( 3cos3x−4sin3x ).

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