What is a derivative?
GeneralClass 10CBSEAnswered 25 May 2026
Answer
A derivative tells you how fast something is changing at any specific moment.
Simple idea: if a car travels 100 km in 2 hours, average speed = 50 km/h. But at some moments it was slower, others faster. A derivative gives the exact speed at any single instant, not just the average.
Formally, the derivative of a function f(x) measures the rate of change of f with respect to x. Geometrically, it gives you the slope of the curve at any single point.
Position, velocity, acceleration are connected by derivatives:
- Derivative of position → velocity (rate of change of position)
- Derivative of velocity → acceleration (rate of change of velocity)
Applications across fields:
- Physics: force is the derivative of momentum
- Economics: marginal cost is the derivative of total cost
- Biology: population growth rate is the derivative of population size
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