Find`f'(x). if f(x) = e^x-logx-sinx`

Answer

To find the derivative \( f'(x) \) of the function \( f(x) = e^x - \log x - \sin x \), we will differentiate each term separately.

### Step-by-Step Solution:

1. **Identify the function**:
\[ f(x) = e^x - \log x - \sin x \]

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

3. **Combine the derivatives**:
Now, we can combine the derivatives of each term:
\[ f'(x) = e^x - \frac{1}{x} - \cos x \]

### Final Answer:
Thus, the derivative \( f'(x) \) is:
\[ f'(x) = e^x - \frac{1}{x} - \cos x \]