# What are the derivatives of the inverse trigonometric functions?

##### 1 Answer

See below.

#### Explanation:

One useful thing to notice is that the derivatives of all inverse "co" functions are equivalent to the derivatives of the original inverse function, but have a negative added.

Here's a proof for the derivative of the inverse sine function, if you want to avoid memorization. All the other ones can be proved in the same way.

Differentiating

We need to get rid of

Recalling that

Thus,

I recommend that you commit these integrals to memory- they will help you when you are learning the trig. substitution.