If `y=log _(e) x+sin x+e^(x) `then `(dy)/(dx)` is:

Options

A. `1/x +sin x+ e^(x)`
B. `-(1)/(x^(2))-cos x +e^(x)`
C. `1/x+ cos x+e^(x)`
D. `-(1)/(x^(2))-sin +e^(x)`

Explanation

To find the derivative \( \frac{dy}{dx} \) for the function \( y = \log_e x + \sin x + e^x \), we will differentiate each term separately.

### Step-by-step Solution:

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

2. **Differentiate each term**:
- The derivative of \( \log_e x \) (which is the natural logarithm) is:
\[ \frac{d}{dx}(\log_e x) = \frac{1}{x} \]
- The derivative of \( \sin x \) is:
\[ \frac{d}{dx}(\sin x) = \cos x \]
- The derivative of \( e^x \) is:
\[ \frac{d}{dx}(e^x) = e^x \]

3. **Combine the derivatives**:
Now, we can combine the derivatives of all three terms:
\[ \frac{dy}{dx} = \frac{1}{x} + \cos x + e^x \]

4. **Final result**:
Thus, the derivative \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = \frac{1}{x} + \cos x + e^x \]