Derivative
The derivative of a function measures how fast its output changes at a single instant, rather than on average over an interval. It is defined as the limit of average rates of change over intervals that shrink to nothing, and it can be read off a graph as the slope of the tangent line at a point. Velocity is the derivative of position, and acceleration is the derivative of velocity.
Why it matters
It turns questions about change, motion, growth, and optimisation into questions that can be computed rather than estimated.
Also written: derivatives, differentiation
Where it comes up
Read about Derivative on Wikipedia
Sources
- Derivative Wikipedia
- Calculus WikipediaRead the overview first if the derivative is the first calculus term you have met.
