Find `dy/dx if y=x^9`

Answer

To find \( \frac{dy}{dx} \) when \( y = x^9 \), we will use the power rule of differentiation. Here are the steps:

### Step-by-Step Solution:

1. **Identify the function**: We start with the function given in the problem, which is:
\[ y = x^9 \]

2. **Apply the power rule**: The power rule states that if \( y = x^n \), then the derivative \( \frac{dy}{dx} \) is given by:
\[ \frac{dy}{dx} = n \cdot x^{n-1} \]
In our case, \( n = 9 \).

3. **Differentiate**: Using the power rule, we differentiate \( y = x^9 \):
\[ \frac{dy}{dx} = 9 \cdot x^{9-1} = 9 \cdot x^8 \]

4. **Final answer**: Therefore, the derivative \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = 9x^8 \]