Find the derivative of given function w.r.t. corresponding independent variable
`y=x^(2)+sin x`

Options

A. `2x+sin x`
B. `2x sin x`
C. `2x+cos x`
D. `2x cos x`

Answer

To find the derivative of the function \( y = x^2 + \sin x \) with respect to the independent variable \( x \), we will follow these steps:

### Step-by-Step Solution

1. **Identify the function**: We have \( y = x^2 + \sin x \).

2. **Differentiate the function**: We need to find \( \frac{dy}{dx} \). This involves differentiating each term in the function separately.

- **Differentiate \( x^2 \)**:
- Using the power rule, if \( y = x^n \), then \( \frac{dy}{dx} = n \cdot x^{n-1} \).
- Here, \( n = 2 \), so \( \frac{d}{dx}(x^2) = 2 \cdot x^{2-1} = 2x \).

- **Differentiate \( \sin x \)**:
- The derivative of \( \sin x \) is \( \cos x \).
- Thus, \( \frac{d}{dx}(\sin x) = \cos x \).

3. **Combine the derivatives**: Now, we add the derivatives of the individual terms together:
\[ \frac{dy}{dx} = \frac{d}{dx}(x^2) + \frac{d}{dx}(\sin x) = 2x + \cos x. \]

4. **Final result**: Therefore, the derivative of the function \( y = x^2 + \sin x \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 2x + \cos x. \]

### Summary
The derivative of the function \( y = x^2 + \sin x \) with respect to \( x \) is \( 2x + \cos x \).