AP Calculus AB: Key Concepts & Formulas

What is the limit definition of the derivative f'(x)?

f'(x) = lim(h->0) [f(x+h) - f(x)] / h

Under what two specific indeterminate forms can L'Hôpital's Rule be applied directly?

0/0 or infinity / infinity

What are the three conditions required for a function f(x) to be continuous at x = c?

1) f(c) is defined; 2) lim(x->c) f(x) exists; 3) lim(x->c) f(x) = f(c)

State the Intermediate Value Theorem (IVT).

If f is continuous on [a, b], then for any value k between f(a) and f(b), there exists at least one c in (a, b) such that f(c) = k.

What is the derivative of x^n with respect to x according to the Power Rule?

nx^(n-1)

State the Product Rule for the derivative of f(x)g(x).

f'(x)g(x) + f(x)g'(x)

State the Quotient Rule for the derivative of f(x)/g(x).

[g(x)f'(x) - f(x)g'(x)] / [g(x)]^2

What is the derivative of the composite function f(g(x))?

f'(g(x)) * g'(x)

When using implicit differentiation on an equation containing y, what must you multiply by whenever you differentiate a y-term?

dy/dx (or y')

If the radius of a circle is increasing at a rate of dr/dt, what is the rate of change of the area A?

dA/dt = 2 * pi * r * (dr/dt)