Find the derivative if f(x)= e^-3x times sin(4x) use the product rule.

Answer 1

d/dx [e^-(3x) ] [ sin (4 x) ]

= [e^-(3x) ] d/dx [ sin (4 x) ]
+ [ sin (4 x) ] d/dx [e^-(3x) ]

= [e^-(3x) ][4 cos (4x) ]
+ [ sin (4 x) ][ -3 e^-(3x) ]

= e^-(3x)[ 4 cos (4x) -3 sin (4x) ]