Ap Calc Trig rules

Derivative of a^x

a^x ln a

derivative of ln a

a’ / a

derivative of sin(x)

cos(x)

derivative of cos(x)

-sin(x)

derivative of tan(x)

sec^2(x)

derivative of csc(x)

-csc(x)cot(x)

derivative of sec(x)

sec(x)tan(x)

derivative of cot(x)

-csc²(x)

When are trig derivatives negative?

When the trig function you are taking a derivative of starts with "c" such as cos(x), csc(x) or cot(x).

antiderivative of sin(x)

-cos(x)+C

antiderivative of cos(x)

sin(x)+C

antiderivative of tan(x)

-ln|cos(x)|+C

antiderivative of csc(x)

-ln|csc(x)+cot(x)|+C

antiderivative of sec(x)

ln|sec(x)+tan(x)|+C

antiderivative of cot(x)

ln|sin(x)|+C

antiderivative of sec²(x)

tan(x)+C

antiderivative of csc²(x)

-cot(x)+C

antiderivative of sec(x)tan(x)

sec(x)

antiderivative of csc(x)cot(x)

-csc(x)+C

antiderivative of e^u

(e^u*1/u)+C

antiderivative of 1/u

ln|u|+C