Find the derivatives of the following (1-3) functions :
f(x) = x+a

Answer

To find the derivative of the function \( f(x) = x + a \), we will follow these steps:

### Step 1: Identify the function
The given function is:
\[ f(x) = x + a \]
Here, \( x \) is the variable and \( a \) is a constant.

### Step 2: Apply the derivative rules
According to the rules of differentiation:
1. The derivative of \( x^n \) (where \( n \) is a constant) is \( n \cdot x^{n-1} \).
2. The derivative of a constant is \( 0 \).

### Step 3: Differentiate each term
- For the term \( x \):
- The power of \( x \) is \( 1 \), so using the power rule:
\[ \frac{d}{dx}(x) = 1 \cdot x^{1-1} = 1 \cdot x^0 = 1 \]

- For the term \( a \):
- Since \( a \) is a constant:
\[ \frac{d}{dx}(a) = 0 \]

### Step 4: Combine the derivatives
Now, we combine the derivatives of both terms:
\[ f'(x) = \frac{d}{dx}(x) + \frac{d}{dx}(a) = 1 + 0 = 1 \]

### Final Answer
Thus, the derivative of the function \( f(x) = x + a \) is:
\[ f'(x) = 1 \]

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