Find `dy/dx if x-2y=0`

Answer

To find \( \frac{dy}{dx} \) for the equation \( x - 2y = 0 \), we will follow these steps:

### Step 1: Start with the given equation
The equation we have is:
\[ x - 2y = 0 \]

### Step 2: Differentiate both sides with respect to \( x \)
We will differentiate the left side and the right side of the equation with respect to \( x \):
\[ \frac{d}{dx}(x) - \frac{d}{dx}(2y) = \frac{d}{dx}(0) \]

### Step 3: Apply the differentiation rules
The differentiation of \( x \) with respect to \( x \) is \( 1 \). For \( 2y \), we apply the product rule:
\[ \frac{d}{dx}(2y) = 2 \cdot \frac{dy}{dx} \]
So, the differentiation gives us:
\[ 1 - 2 \frac{dy}{dx} = 0 \]

### Step 4: Solve for \( \frac{dy}{dx} \)
Now, we can rearrange the equation to solve for \( \frac{dy}{dx} \):
\[ 1 = 2 \frac{dy}{dx} \]
Dividing both sides by \( 2 \):
\[ \frac{dy}{dx} = \frac{1}{2} \]

### Final Answer
Thus, the value of \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = \frac{1}{2} \]

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