Compare the possible meanings
| Notation | Typical meaning | How to identify it |
|---|---|---|
df/dx | Ordinary derivative | One independent variable or total dependence |
∂f/∂x | Partial derivative | Several independent variables |
df | Differential | Linearized change |
dx | Integration measure or differential | Context determines role |
Examples
- For f(x)=x², df/dx=2x.
- For f(x,y)=x²y, ∂f/∂x=2xy.
- The total differential is df=fx dx+fy dy.
How to decide
Ask whether other independent variables are being held constant. If yes, ∂ is normally the correct operator.
How to verify the interpretation
List the independent variables and differentiate the expression explicitly.