Calculus Introduction
Derivatives
Measure how an output changes near an input.
Before this
The intuition
A derivative describes local sensitivity. It tells you approximately how much the output changes for a small change in the input.
A concrete example
For f(x) = x², the derivative is 2x. At x = 3, a small input increase of 0.01 gives an approximate output increase of 6 × 0.01 = 0.06.
What to remember
A derivative is local. A large step may behave differently from the local approximation.
Check your understanding
Where is the derivative of x² zero?
Reveal explanation
At x = 0, the bottom of this particular bowl.