Find the derivative of `f(x) = tan x + "sin" x + x^(5)`

Answer

To find the derivative of the function \( f(x) = \tan x + \sin x + x^5 \), we will differentiate each term separately and then combine the results.

### Step-by-Step Solution:

1. **Identify the function**:
\[ f(x) = \tan x + \sin x + x^5 \]

2. **Differentiate each term**:
- The derivative of \( \tan x \) is \( \sec^2 x \).
- The derivative of \( \sin x \) is \( \cos x \).
- The derivative of \( x^5 \) is \( 5x^4 \).

3. **Combine the derivatives**:
\[ f'(x) = \frac{d}{dx}(\tan x) + \frac{d}{dx}(\sin x) + \frac{d}{dx}(x^5) \]
\[ f'(x) = \sec^2 x + \cos x + 5x^4 \]

4. **Final answer**:
\[ f'(x) = \sec^2 x + \cos x + 5x^4 \]