What do Delta x / Delta y Mean?
The Greek letter Δ means “the change in” a variable. It’s usually used to mean a change in either the x-variable or y-variable:
- x: a horizontal value on the x-axis.
- Δx: a horizontal change (from point “a” to point “b” on the x-axis)
- y: a vertical value on the y-axis.
- Δy: a vertical change (from point “a” to point “b” on the y-axis)
Delta x / Delta y and The Slope
A linear (straight line) function has the equation
y = mx + b.
The “m” in the formula is the slope. In beginning algebra, you usually find the slope with the formula
slope = rise over run.
- Rise = change in y-values (from point a to point b).
- Run = change in x-values (from point a to point b).
Delta x / Delta y and Derivatives
The notation Δ x is used in calculus (especially physics) to mean tiny changes or very small increments. These tiny changes (close to zero) allow us to find the derivative, which is the slope at a point.
A similar notation is dy/dx, which means “derivative”. However, there’s a big difference between Δy / Δx, and dy/dx:
- Δy / Δx, can be interpreted as meaning a quotient of small differences in y and x. The quotient is the answer to a division problem . For example, in the problem 10 / 5, 2 is the quotient..
- dy/dx means derivative and you can’t interpret it as a quotient of two numbers dy and dx.
The notation dy/dx is called Leibnitz notation. Another notation which means the same thing is f′ (prime notation), which avoids the confusion with a “quotient” .
Calculus suffers from a lack of consistent notation, partly due to so many different mathematicians working separately in the early years of its development. There are other various meanings for delta (both upper- and lower-case) including “discriminant”. See: Delta meaning.
 Open University. 3.3.3 Multiplication and Division Math Terminology.
 Stony Brook Calculus Materials: Calculus I Handouts.