How to solve
A partial derivative measures how a multivariable function changes when one input moves and the others stay fixed. Treat every other variable as a constant, then differentiate with the ordinary single-variable rules in the chosen direction.
Steps
- Choose the variable of differentiation; treat the others as constants.
- Apply the ordinary power rule (and product rule if needed) in that variable.
- Leave other variables in the result where they belong.
Example
If f(x, y) = 3x²y, find f_x.
- Treat y as constant; differentiate in x: f_x = 6xy.
Answer: 6xy
How to type answers
- Enter like 6x y^2 or 3y^2
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