Find `(d^(2)y)/(dx^(2))` when
`y=e^(x)+sinx`

Answer

To find the second derivative \(\frac{d^2y}{dx^2}\) for the function \(y = e^x + \sin x\), we will follow these steps:

### Step 1: Write down the function
We start with the given function:
\[ y = e^x + \sin x \]

### Step 2: Find the first derivative
We differentiate \(y\) with respect to \(x\):
\[ \frac{dy}{dx} = \frac{d}{dx}(e^x) + \frac{d}{dx}(\sin x) \]
Using the known derivatives:
- The derivative of \(e^x\) is \(e^x\).
- The derivative of \(\sin x\) is \(\cos x\).

Thus, we have:
\[ \frac{dy}{dx} = e^x + \cos x \]

### Step 3: Find the second derivative
Now, we differentiate \(\frac{dy}{dx}\) to find the second derivative:
\[ \frac{d^2y}{dx^2} = \frac{d}{dx}(e^x + \cos x) \]
Again, using the known derivatives:
- The derivative of \(e^x\) is \(e^x\).
- The derivative of \(\cos x\) is \(-\sin x\).

So, we have:
\[ \frac{d^2y}{dx^2} = e^x - \sin x \]

### Final Answer
Thus, the second derivative is:
\[ \frac{d^2y}{dx^2} = e^x - \sin x \]

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