Question

Is there an easy way to memorize the derivatives of inverse trigonometric functions?

Answer 1

The way is not to memorize.
The easiest way is to derive the formulae.
For e.g

`y=cos^-1(x)`
then
`x=cosy`
`dx = -siny dy`
`dy/dx = -1/sin(y)`
`dy/dx =-1/sqrt(1-x^2)`

Answer 2

There is some way to memorize, though you shouldn't have to. Knowing how to derive it is helpful for figuring them out again (maybe your internet goes out... I dunno). You can do it in "regular" and "co-" pairs.

While `(d(arc tanx))/dx = 1/(1+x^2)`,

`(d(arc cotx))/dx = -1/(1+x^2)`.

---

While `(d(arc sinx))/dx = 1/sqrt(1-x^2)`,

`(d(arc cosx))/dx = -1/sqrt(1-x^2)`.

---

While `(d(arc secx))/dx = 1/(absxsqrt(x^2-1))`,

`(d(arc cscx))/dx = -1/(absxsqrt(x^2-1))`.

Now you only have to remember three of them. "co-" implies a reversed sign.