AP Calculus AB Exam Flashcards

Vocabulary flashcards for key calculus concepts and formulas.

Limit of sin(x)/x as x approaches 0

lim (x->0) sin(x) / x = 1

d/dx sin(x) = cos(x)

Derivative of sin(x)

d/dx cos(x) = -sin(x)

Derivative of cos(x)

d/dx tan(x) = sec^2(x)

Derivative of tan(x)

d/dx sec(x) = sec(x)tan(x)

Derivative of sec(x)

d/dx csc(x) = -csc(x)cot(x)

Derivative of csc(x)

d/dx cot(x) = -csc^2(x)

Derivative of cot(x)

d/dx ln(x) = 1/x

Derivative of ln(x)

d/dx e^x = e^x

Derivative of e^x

d/dx arcsin(x) = 1 / sqrt(1-x^2)

Derivative of arcsin(x)

d/dx arccos(x) = -1 / sqrt(1-x^2)

Derivative of arccos(x)

d/dx arctan(x) = 1 / (1+x^2)

Derivative of arctan(x)

Power Rule

The rule that states d/dx[x^n] = nx^(n-1)

Product Rule

The rule that states d/dx[f(x) * g(x)] = f'(x)g(x) + f(x)g'(x)

Quotient Rule

The rule that states d/dx[f(x) / g(x)] = [g(x)f'(x) - f(x)g'(x)] / [g(x)]^2

Chain Rule

The rule that states d/dx[f(g(x))] = f'(g(x)) * g'(x)

∫sin(x) dx = -cos(x) + C

Integral of sin(x)

∫cos(x) dx = sin(x) + C

Integral of cos(x)

∫sec^2(x) dx = tan(x) + C

Integral of sec^2(x)

∫sec(x)tan(x) dx = sec(x) + C

Integral of sec(x)tan(x)

∫csc(x)cot(x) dx = -csc(x) + C

Integral of csc(x)cot(x)

∫csc^2(x) dx = -cot(x) + C

Integral of csc^2(x)

∫(1/x) dx = ln|x| + C

Integral of 1/x

FTC

An element of the Fundamental Theorem of Calculus