When a function depends on more than one variable, you can ask 'what's the slope in the x-direction?' or 'in the y-direction?'. Each is a partial derivative.
Partial derivative notation
∂f/∂x
Slope in the x-direction, holding y constant
Try it
f(x, y) = x²y + 3y. Find ∂f/∂x.
Treat y as a constant: ∂f/∂x = 2xy.