Find \( \frac{d y}{d x} \) for the following function. \( y=3 \sin x+7 \cos x \) \( \frac{d y}{d x}=\square \)

1. We start with the function: \[ y = 3 \sin x + 7 \cos x \] 2. The derivative of \(\sin x\) is \(\cos x\) and the derivative of \(\cos x\) is \(-\sin x\). 3. Applying the derivative term by term: \[ \frac{dy}{dx} = 3 \frac{d}{dx}(\sin x) + 7 \frac{d}{dx}(\cos x) \] \[ \frac{dy}{dx} = 3 \cos x + 7(-\sin x) \] \[ \frac{dy}{dx} = 3 \cos x - 7\sin x \] 4. Thus, the derivative is: \[ \frac{dy}{dx} = 3 \cos x - 7\sin x \]