Find the derivatives of the following (1-3) functions :
`y=x^(2)`

Answer

To find the derivative of the function \( y = x^2 \), we can follow these steps:

### Step 1: Identify the function
The function given is:
\[ y = x^2 \]

### Step 2: Apply the power rule
The power rule states that if \( y = x^n \), then the derivative \( \frac{dy}{dx} \) (or \( y' \)) is given by:
\[ \frac{dy}{dx} = n \cdot x^{n-1} \]

In our case, \( n = 2 \).

### Step 3: Substitute \( n \) into the power rule
Now, we substitute \( n = 2 \) into the formula:
\[ \frac{dy}{dx} = 2 \cdot x^{2-1} \]

### Step 4: Simplify the expression
This simplifies to:
\[ \frac{dy}{dx} = 2 \cdot x^{1} \]
\[ \frac{dy}{dx} = 2x \]

### Final Answer
Thus, the derivative of the function \( y = x^2 \) is:
\[ \frac{dy}{dx} = 2x \]

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