ap calc bc

Definition of Derivative

The instantaneous rate of change of a function with respect to its variable. It is the slope of the tangent line to the function at a given point. Calculated as f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}.

Definition of Integral

The reverse process of differentiation. Finding a function given its derivative. Denoted as \int f(x) dx = F(x) + C, where F'(x) = f(x) and C is the constant of integration.

Chain Rule

Used to find the derivative of a composite function. If y = f(g(x)), then \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}, where u = g(x).

Product Rule

Used to find the derivative of a product of two functions. If h(x) = f(x)g(x), then h'(x) = f'(x)g(x) + f(x)g'(x).