Find `dy/dx if y=2 sin x - cos x `

Answer

To find \(\frac{dy}{dx}\) for the function \(y = 2 \sin x - \cos x\), we will differentiate the function with respect to \(x\).

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = 2 \sin x - \cos x \]

2. **Differentiate each term**:
- The derivative of \(2 \sin x\):
- The constant \(2\) remains as it is.
- The derivative of \(\sin x\) is \(\cos x\).
\[ \frac{d}{dx}(2 \sin x) = 2 \cdot \cos x \]

- The derivative of \(-\cos x\):
- The derivative of \(\cos x\) is \(-\sin x\), so the derivative of \(-\cos x\) will be:
\[ \frac{d}{dx}(-\cos x) = -(-\sin x) = \sin x \]

3. **Combine the derivatives**:
\[ \frac{dy}{dx} = 2 \cos x + \sin x \]

4. **Final result**:
\[ \frac{dy}{dx} = 2 \cos x + \sin x \]