Find `dy/dx if y=x^4-x^7`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = x^4 - x^7\), we will use the power rule of differentiation. The power rule states that if \(y = x^n\), then \(\frac{dy}{dx} = n \cdot x^{n-1}\).

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = x^4 - x^7 \]

2. **Differentiate each term separately**:
- For the first term \(x^4\):
\[ \frac{d}{dx}(x^4) = 4 \cdot x^{4-1} = 4x^3 \]
- For the second term \(-x^7\):
\[ \frac{d}{dx}(-x^7) = -7 \cdot x^{7-1} = -7x^6 \]

3. **Combine the derivatives**:
\[ \frac{dy}{dx} = 4x^3 - 7x^6 \]

Thus, the final result is:
\[ \frac{dy}{dx} = 4x^3 - 7x^6 \]