Common Derivatives & Integrals (AP Calculus AB)

derivative of sin(x)

cos(x)

derivative of cos(x)

-sin(x)

derivative of tan(x)

sec^2(x)

derivative of cot(x)

-csc^2(x)

derivative of sec(x)

sec(x)tan(x)

derivative of csc(x)

-csc(x)cot(x)

derivative of arcsin(x)

1/sqrt(1-x^2)

derivative of arccos(x)

-1/sqrt(1-x^2)

derivative of arctan(x)

1/(1+x^2)

derivative of arccot(x)

-1/(1+x^2)

derivative of arcsec(x)

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

derivative of arccsc(x)

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

derivative of a^x

a^x(ln(a))

derivative of ln(x)

1/x, x>0

derivative of ln(|x|)

1/x, x!=0

derivative of e^x

e^x

derivative of x

1

derivative of 1/x

-1/(x^2)

derivative of sqrt(x)

1/(2sqrt(x))

derivative of log_a(x)

1/(x ln(a))

derivative of c

0

derivative of cx

c

derivative of x^n

nx^(n-1)

derivative of cx^n

cnx^(n-1)

∫(1/√(a²-u²)du

arcsin(u/a)+C

∫(1/(|u|√(u²-a²))du

(1/a)arcsec(|u|/a)+C

∫(1/(u²-a²)du

(1/a)arctan(|u|/a)+C

∫(tan(x))dx

ln|sec(x)|+C

sin(2x)

2sin(x)cos(x)

cos(2x)

cos^2(x)-sin^2

tan(2x)

2tan(x)/[1-tan^2(x)]