Thu gọn A

To simplify the expression given in the problem:

### Given
\[ A = 9x^2 - \left(-\frac{1}{3}\right)xy^3 \]

### a) Simplifying A

1. Rewrite the expression:
\[ A = 9x^2 + \frac{1}{3}xy^3 \]

2. To combine or factor the terms, notice that there is no common factor that can simplify further. So, the final simplified expression remains as:
\[ A = 9x^2 + \frac{1}{3}xy^3 \]

### b) Finding the derivative

To find the partial derivatives with respect to \(x\) and \(y\):

1. **Partial derivative with respect to x**:
\[
\frac{\partial A}{\partial x} = \frac{\partial}{\partial x}(9x^2) + \frac{\partial}{\partial x}\left(\frac{1}{3}xy^3\right)
= 18x + \frac{1}{3}y^3
\]

2. **Partial derivative with respect to y**:
\[
\frac{\partial A}{\partial y} = \frac{\partial}{\partial y}(9x^2) + \frac{\partial}{\partial y}\left(\frac{1}{3}xy^3\right)
= 0 + \frac{1}{3} \cdot 3xy^2
= xy^2
\]

### Conclusion
- **Simplified A**:
\[ A = 9x^2 + \frac{1}{3}xy^3 \]

- **Partial Derivatives**:
\[
\frac{\partial A}{\partial x} = 18x + \frac{1}{3}y^3
\]
\[
\frac{\partial A}{\partial y} = xy^2
\]

If you need any further calculations or explanations, feel free to ask!