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Given f(x) = 7(e^2x) * (sin(3x)), find f'(x)

f(x) = 7e^2x sin(3x) Chain rule: f(x) = uv → f'(x) = u'v + uv' u = 7e^2x u' = 14e^2x v = sin(3x) v' = 3cos(3x) f'(x) = 14e^2xsin(3x) + 7e^2x 3cos(3x) f'(x) = 7e^2x ( 2 sin (3x) + 3 cos (3x) )

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