Find the derivative of the following function. \[ y=e^{-x} \sin x \]

Step 1 ：We are given the function \(y=e^{-x} \sin x\).

Step 2 ：We need to find the derivative of this function.

Step 3 ：To do this, we will use the product rule and the chain rule.

Step 4 ：The product rule is used when differentiating the product of two functions, and the chain rule is used when differentiating the composition of two functions.

Step 5 ：In this case, the function is the product of \(e^{-x}\) and \(\sin x\), so we will need to use the product rule.

Step 6 ：The function \(e^{-x}\) is also the composition of \(e^x\) and \(-x\), so we will need to use the chain rule to differentiate it.

Step 7 ：Applying the product rule, we get \(dy/dx = -e^{-x}\sin x + e^{-x}\cos x\).

Step 8 ：\(\boxed{-e^{-x}\sin x + e^{-x}\cos x}\) is the final answer.