Find `dy/dx if y=5x^7`

Answer

To find \( \frac{dy}{dx} \) for the function \( y = 5x^7 \), we will use the power rule of differentiation. Here are the steps:

### Step 1: Identify the function
We have the function:
\[ y = 5x^7 \]

### Step 2: Apply the power rule
The power rule states that if \( y = ax^n \), then:
\[ \frac{dy}{dx} = n \cdot ax^{n-1} \]
In our case, \( a = 5 \) and \( n = 7 \).

### Step 3: Differentiate the function
Using the power rule:
\[ \frac{dy}{dx} = 7 \cdot 5x^{7-1} \]
This simplifies to:
\[ \frac{dy}{dx} = 35x^6 \]

### Step 4: Write the final answer
Thus, the derivative \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = 35x^6 \]

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