Partial Derivatives

Slopes in one direction

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\partial f/\partial x$: the slope in the $x$-direction, holding $y$ fixed.
• Compute it by differentiating normally and treating the other variables as constants.
• Each direction can have a different slope.

Steps

1. Holding one variable still
2. Evaluate a partial
3. Slicing the landscape
4. Mixed partials
5. Small changes add up
6. The other direction