#### Answer

$y'=e^{6x}(\cos x+6\sin x)$

#### Work Step by Step

$y=e^{6x}\sin x$
Start the differentiation process by applying the product rule:
$y'=e^{6x}(\sin x)'+(e^{6x})'\sin x=...$
Evaluate the indicated derivatives and simplify:
$...=e^{6x}\cos x+6e^{6x}\sin x=...$
Take out common factor $e^{6x}$:
$...=e^{6x}(\cos x+6\sin x)$