# How do you find the derivative of #(ln tan(x))^2#?

##### 1 Answer

How? Use the chain rule -- twice.

And simplify the answer. (Often simplifying is the tricky part.)

The derivative of some stuff squared is two times the stuff, times the derivative of that stuff.

Formally : the derivative of

In this case the "inside stuff", the

The derivative of the

Formally : the derivative of

Finally, we need to know the derivative of

The derivative of

Now, we've finished the calculus, but we can re-write our answer in simpler form.

and

The second equality wouldn't be helpful, except that

Therefore we can re-write the derivative using:

Which is surely more simply written as

So

The derivative of

(If there's any advantage to it, we could also re-write