Question

найти y'''(x0)
y=e^x *sin2x x0=0

Answer 1

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Answer 2

$y=e^xsin2x \ y'=e^xsin2x+2e^xcos2x \ y''=(e^xsin2x+2e^xcos2x)'=e^xsin2x+2e^xcos2x+ \ +2e^xcos2x-4e^xsin2x=4e^xcos2x-3e^xsin2x \ y'''=(4e^xcos2x-3e^xsin2x)'= 4e^xcos2x-8e^xsin2x- \ -3e^xsin2x-6e^xcos2x=-11e^xsin2x-2e^xcos2x \ y'''(x_0)=y'''(0)=-11e^0sin0-2e^0cos0=-2 \ y'''(0)=-2$