AP Calc AB Trig Derivatives

sinx

cosx

cosx

-sinx

tanx

sec²x

cotx

-csc²x

secx

secx*tanx

cscx

-cscx*cotx

arcsinx

1

---

√(1-x²)

arccosx

-1

---

√(1-x²)

arctanx

1

---

1+x²

arccotx

-1

---

1+x²

arcsecx

1

---

|x|√(x²-1)

arccscx

-1

---

|x|√(x²-1)

How are the arctrig derivatives related?

For each of the pairs of derivatives (arcsin/arccos, arctan/arccot, and arcsec/arccsc) the one that starts with co is negative and the one that does not is positive. Every other part of the equation is the same.

How can you apply the chain rule to arctrig?

The derivative of the inside function goes in the numerator, while the derivative of the outside function goes in the denominator.