If `y= sin x+cos x
then (d^(2)y)/(dx^(2))` is :-

Options

A. `sin x- cos x`
B. `cos x- sin x`
C. `-(sin x+ cos x)`
D. None of these

Explanation

To find the second derivative of the function \( y = \sin x + \cos x \), we will follow these steps:

### Step 1: Differentiate \( y \) to find the first derivative \( \frac{dy}{dx} \)

Given:
\[ y = \sin x + \cos x \]

We differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \frac{d}{dx}(\sin x) + \frac{d}{dx}(\cos x) \]

Using the derivatives of sine and cosine:
\[ \frac{dy}{dx} = \cos x - \sin x \]

### Step 2: Differentiate \( \frac{dy}{dx} \) to find the second derivative \( \frac{d^2y}{dx^2} \)

Now we differentiate \( \frac{dy}{dx} \):
\[ \frac{d^2y}{dx^2} = \frac{d}{dx}(\cos x - \sin x) \]

Using the derivatives of cosine and sine:
\[ \frac{d^2y}{dx^2} = -\sin x - \cos x \]

### Step 3: Simplify the expression

We can rewrite the expression:
\[ \frac{d^2y}{dx^2} = -(\sin x + \cos x) \]

### Final Result

Thus, the second derivative \( \frac{d^2y}{dx^2} \) is:
\[ \frac{d^2y}{dx^2} = -(\sin x + \cos x) \]

### Conclusion

The correct answer is:
\[ \frac{d^2y}{dx^2} = -(\sin x + \cos x) \]

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