Find `(dy)/(dx)` for the following :
`y=x`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = x\), we will follow the steps of differentiation.

### Step-by-Step Solution:

1. **Identify the function**: We have the function \(y = x\).

2. **Differentiate the function**: To differentiate \(y\) with respect to \(x\), we use the basic rule of differentiation for algebraic functions. The rule states that if \(y = x^n\), then \(\frac{dy}{dx} = n \cdot x^{n-1}\).

3. **Apply the rule**: In our case, \(y = x\) can be rewritten as \(y = x^1\). Here, \(n = 1\).

4. **Differentiate**: Using the differentiation rule:
\[ \frac{dy}{dx} = 1 \cdot x^{1-1} = 1 \cdot x^0 = 1 \]

5. **Final answer**: Therefore, \(\frac{dy}{dx} = 1\).

### Summary:
The derivative of \(y = x\) with respect to \(x\) is \(\frac{dy}{dx} = 1\).

---