How do you differentiate #f(x)=csc(ln(1-x^2)) # using the chain rule?
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
Finally lets look at
Now substituting in the functions obtained previously we finally end up with:
And that is our final answer.