Find `dy/dx if y= ax^2`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = ax^2\), we will follow these steps:

### Step 1: Identify the function
We start with the function:
\[ y = ax^2 \]
where \(a\) is a constant.

### Step 2: Apply the differentiation rule
We will use the power rule of differentiation, which states that if \(y = x^n\), then:
\[ \frac{dy}{dx} = nx^{n-1} \]
In our case, we have \(y = ax^2\). Here, \(a\) is a constant and does not change with respect to \(x\).

### Step 3: Differentiate the function
Using the power rule, we differentiate \(y = ax^2\):
\[ \frac{dy}{dx} = a \cdot \frac{d}{dx}(x^2) \]
Now, we apply the power rule to \(x^2\):
\[ \frac{d}{dx}(x^2) = 2x^{2-1} = 2x \]
Thus, substituting this back, we have:
\[ \frac{dy}{dx} = a \cdot 2x = 2ax \]

### Step 4: Write the final answer
Therefore, the derivative \(\frac{dy}{dx}\) is:
\[ \frac{dy}{dx} = 2ax \]

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