# What is the derivative of #f(x)=csc^-1(x)# ?

##### 1 Answer

**Process:**

1.)

First we will rewrite the equation in a form that is easier to work with.

Take the cosecant of both sides:

2.)

Rewrite in terms of sine:

3.)

Solve for

4.)

5.)

6.)

Now, taking the derivative should be easier. It's now just a matter of chain rule.

We know that

So, take the derivative of the outside function, then multiply by the derivative of

7.)

The derivative of

8.)

Simplifying 8. gives us:

9.)

To make the statement a little prettier, we can bring the square of

10.)

Simplifying yields:

11.)

And there is our answer. Remember, derivatives problems involving inverse trig functions are mostly an exercise in your knowledge of trig identities. Use them to break down the function into a form that's easy to differentiate.