The derivative of a function at a point is the rate at which the function's value changes as its input changes. It is defined as the limit of the difference quotient as the interval approaches zero.
Difference Quotient: The expression $\frac{f(x+h)-f(x)}{h}$, which approximates the slope of the secant line between two points on a graph.
Power Rule: A basic rule for differentiation stating that if $f(x)=x^n$, then $f'(x)=nx^{n-1}$.
Tangent Line: A straight line that touches a curve at exactly one point and has the same slope as the curve at that point.