Find `dy/dx if y=5x`

Answer

To find \( \frac{dy}{dx} \) for the function \( y = 5x \), we will follow these steps:

### Step 1: Identify the function
We have the function:
\[ y = 5x \]

### Step 2: Differentiate with respect to \( x \)
To find \( \frac{dy}{dx} \), we need to differentiate \( y \) with respect to \( x \). The differentiation of a function gives us the rate of change of that function.

### Step 3: Apply the differentiation rule
The differentiation rule states that the derivative of a constant multiplied by a variable is simply the constant. Here, the constant is \( 5 \) and the variable is \( x \).

So, we differentiate:
\[ \frac{dy}{dx} = \frac{d}{dx}(5x) \]

### Step 4: Calculate the derivative
Using the differentiation rule:
\[ \frac{dy}{dx} = 5 \cdot \frac{d}{dx}(x) \]
The derivative of \( x \) with respect to \( x \) is \( 1 \):
\[ \frac{dy}{dx} = 5 \cdot 1 = 5 \]

### Final Answer
Thus, the value of \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = 5 \]

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