# How do you differentiate #f(x)=csc(ln(1-x^2)) # using the chain rule?

##### 1 Answer

#### Answer:

#### Explanation:

Essentially the chain rule rule states that

This example is obviously a bit more complicated because what we have here is a function inside a of function inside another function, or more formally:

Let us define:

Let's start by looking at the inner most function:

Differentiating this yields

Now let's look at

Differentiating the logarithm and applying the chain rule to

gives us

Substituting

Finally lets look at

Note that

So differentiating

Now substituting in the functions obtained previously we finally end up with:

And that is our final answer.