AP Calculus AB Derivatives

sin(x)

cos(x)

cos(x)

-sin(x)

tan(x)

sec^2(x)

cot(x)

-csc^2(x)

sec(x)

sec(x)tan(x)

csc(x)

-csc(x)cot(x)

arcsin(x)

1 / sqrt(1 - x^2)

arccos(x)

-1 / sqrt(1 - x^2)

arctan(x)

1 / (1 + x^2)

arccot(x)

-1 / (1 + x^2)

arcsec(x)

1 / (|x|sqrt(x^2 - 1))

arccsc(x)

-1 / (|x|sqrt(x^2 - 1))

ln(x)

1 / x

e^x

e^x

log_b(x)

1 / (x ln(b))

a^x

a^x ln(a)

f(x) at point a given f(a) = b (define using inverse)

1 / f^(-1)'(b)