Differentiate and simplify: f(x) = (sinx)(e^-2x)

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ttpp1124
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Homework Statement
can someone confirm my work?
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Handwritten product rule working differentiating f(x) = (sin x)(e^-2x), with steps for d/dx of sin x, d/dx of e^-2x, and the simplified result e^-2x cos(x) - 2e^-2x sin(x).
 

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