Multivariable Calculus

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

  1. Choose the variable of differentiation; treat the others as constants.
  2. Apply the ordinary power rule (and product rule if needed) in that variable.
  3. Leave other variables in the result where they belong.

Example

If f(x, y) = 3x²y, find f_x.

  1. Treat y as constant; differentiate in x: f_x = 6xy.

Answer: 6xy

How to type answers

  • Enter like 6x y^2 or 3y^2
Loading drills…