Math basics › Calculus
What a derivative is
Slope at a point
The derivative is the slope of the tangent line — how fast the function is changing right there.
It comes from the limit
f′(x) = lim as h→0 of (f(x + h) − f(x))/h. Rise over run, with the run shrinking to nothing.
Reading the sign
Positive means rising, negative means falling, zero means a flat spot — a maximum, a minimum, or a pause.