Evaluate differentiation of y with respect to x :
`y=x^(2)-sinx`

Explanation

To evaluate the differentiation of \( y \) with respect to \( x \) for the function \( y = x^2 - \sin x \), we will follow these steps:

### Step 1: Identify the function
The function given is:
\[ y = x^2 - \sin x \]

### Step 2: Differentiate each term
We will differentiate each term in the function separately. The function consists of two terms: \( x^2 \) (an algebraic term) and \( -\sin x \) (a trigonometric term).

1. **Differentiate \( x^2 \)**:
- The differentiation rule for \( x^n \) is \( \frac{d}{dx}(x^n) = n \cdot x^{n-1} \).
- Here, \( n = 2 \), so:
\[ \frac{d}{dx}(x^2) = 2 \cdot x^{2-1} = 2x \]

2. **Differentiate \( -\sin x \)**:
- The differentiation rule for \( \sin x \) is \( \frac{d}{dx}(\sin x) = \cos x \).
- Therefore, the differentiation of \( -\sin x \) is:
\[ \frac{d}{dx}(-\sin x) = -\cos x \]

### Step 3: Combine the results
Now, we combine the results of the differentiation of each term:
\[ \frac{dy}{dx} = \frac{d}{dx}(x^2) - \frac{d}{dx}(\sin x) = 2x - \cos x \]

### Final Result
Thus, the differentiation of \( y \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 2x - \cos x \]

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