| Step | Expression | Explanation |
|---|---|---|
| 1 | ∂/∂x (x/y) | Start with the original function |
| 2 | = 1/y ∂/∂x(x) | Treat y as a constant while differentiating with respect to x |
| 3 | = 1/y × 1 | Differentiate x to get 1 |
| 4 | = 1/y | Multiply by the constant 1/y |
| Step | Expression | Explanation |
|---|---|---|
| 1 | ∂/∂y (x/y) | Start with the original function |
| 2 | = ∂/∂y (x × y⁻¹) | Rewrite x/y as x × y⁻¹ |
| 3 | = x ∂/∂y(y⁻¹) | Treat x as a constant while differentiating with respect to y |
| 4 | = x × -1 × y⁻² | Differentiate y⁻¹ to get -1 × y⁻² |
| 5 | = -x × y⁻² | Simplify -1 × y⁻² to -y⁻² |
| 6 | = -x/y² | Simplify -y⁻² to -1/y² |
| 7 | = -x/y² | Multiply by the constant x |
| 8 | = -x/y² | The partial derivative is -x/y² |