Important Derivatives and Antiderivatives

derivative of sinx

cosx

derivative of cosx

-sinx

derivative of tanx

sec²x

derivative of secx

secxtanx

derivative cotx

-csc²x

derivative of cscx

-cscxcotx

derivative of arcsinx

1/(square root of 1-x²)

derivative of arccos(x)

-1/(square root of 1-x²)

derivative of arctan(x)

1/(1+x²)

derivative of arccot(x)

-1/(1+x²)

derivative of arcsec(x)

1/(|x|(square root of x²-1))

derivative of arccsc(x)

-1/(|x|(square root of x²-1))

derivative of lnx

1/x

antiderivative of lnx

xln(x)-x

antiderivative of cotx

ln |sin(x)|

antiderivative of sinx

-cosx

antiderivative of cosx

sinx

antiderivative of secx

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

When you have the antiderivative of 1/x or it equals natural log, then what happens to the natural log

ln |x|

antiderivative of cscx

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

antiderivative of tan(x)

ln |sec(x)|