Judging by your function, you are to find the derivative in

, right?

So, you have to differentiate using

*the chain rule* and the quotient rule. The numerator is a composition of the sine function and of the linear function (a function of a function). See:

(For lack of confusion, I will use 't' instead of 'x' as the dummy variable.)

and

Once those two are joined as a composition, then we get:

, or in your case

.

This function is then divided by another, and that is why you need the quotient rule.

The chain rule shows us that:

Where, in your case,

.

The derivative of

in

is:

You first differentiate the cosine

and then the function inside and multiply the original,

.

Then, by using the quotient rule:

In your case:

Maybe the expression can be simplified, but it looks nice either way =)

Good luck and remember the chain rule when you differentiate a composition of functions.