Find y' and y" y = e^ax sin beta x

Given y = e^ax sin beta x

For every function h(x) = f(x) * g(x)

h'(x) = f(x) g'(x) + g(x) f'(x)
so,

y' = (e^ax) [(cos beta x)( beta )] + (sin beta x)[(e^ax)(a)]

y" = { (e^ax) [(beta)(-sin beta x) (beta)] } + { [(cos beta x)( beta )] [(e^ax)(a)] } + (sin beta x)[(e^ax) (a)^2 ] + [(e^ax)(a)][(cos beta x)(beta) ]


Hope, this would help !