How do you differentiate #f(x)=1/cossqrt(1/x)# using the chain rule?
The chain rule is used whenever there are functions of functions. In other words, when you have a function of the form;
The chain rule tells us that the derivative of this function is;
The first step to using the chain rule is to identify the separate functions. Lets start by rewriting the given function to make the component functions easier to identify.
Now we have a function of the form;
You can see that if you work backwards plugging these functions into each other, you get the original function back.
We can take the derivative of each of these component functions to get;
Now we apply the chain rule to our function.
Apply the chain rule again.
Take the last derivative.