Differentiate the following w.r.t. x :
`e^(x)+2cosx`

Answer

To differentiate the function \( y = e^x + 2\cos x \) with respect to \( x \), we will apply the rules of differentiation step by step.

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = e^x + 2\cos x \]

2. **Differentiate the first term \( e^x \)**:
The derivative of \( e^x \) with respect to \( x \) is:
\[ \frac{d}{dx}(e^x) = e^x \]

3. **Differentiate the second term \( 2\cos x \)**:
We will use the constant multiple rule and the derivative of \( \cos x \):
\[ \frac{d}{dx}(2\cos x) = 2 \cdot \frac{d}{dx}(\cos x) = 2 \cdot (-\sin x) = -2\sin x \]

4. **Combine the derivatives**:
Now, we can combine the derivatives of both terms:
\[ \frac{dy}{dx} = e^x - 2\sin x \]

5. **Final answer**:
Thus, the derivative of the function \( y = e^x + 2\cos x \) with respect to \( x \) is:
\[ \frac{dy}{dx} = e^x - 2\sin x \]