If `y=sinx+cosx" then "(d^(2)y)/(dx^(2))` is :-

Options

A. `sinx-cosx`
B. `cosx-sinx`
C. `-(sinx+cosx)`
D. None of these

Answer

To solve the problem, we need to find the second derivative of the function \( y = \sin x + \cos x \).

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = \sin x + \cos x \]

2. **First Derivative**:
We need to find the first derivative \( \frac{dy}{dx} \).
\[ \frac{dy}{dx} = \frac{d}{dx}(\sin x) + \frac{d}{dx}(\cos x) \]
Using the derivatives of sine and cosine:
\[ \frac{dy}{dx} = \cos x - \sin x \]

3. **Second Derivative**:
Now, we find the second derivative \( \frac{d^2y}{dx^2} \) by differentiating \( \frac{dy}{dx} \).
\[ \frac{d^2y}{dx^2} = \frac{d}{dx}(\cos x - \sin x) \]
Using the derivatives again:
\[ \frac{d^2y}{dx^2} = -\sin x - \cos x \]

4. **Final Result**:
We can factor out a negative sign:
\[ \frac{d^2y}{dx^2} = -(\sin x + \cos x) \]

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