I'll rewrite this using our trig identity as cosine of x times sine of delta x plus sine of x times cosine of delta x. And then we're going to subtract this sine of x up here minus sine of x, all of that over, let me see if I can draw a relatively straight line, all of that over delta x. So this can be rewritten as being equal to the limit as delta x approaches zero of, let me write this part in red, so that would be cosine of x sine of delta x, all of that over delta x, and then that's going to be plus, I'll do all of this in orange, all I'm doing is I have the sum of things up here divided by delta x, I'm just breaking it up a little bit, plus sine of x cosine of delta x minus sine of x, all of that over delta x, and remember I'm taking the limit of this entire expression. Well the limit of a sum is equal to the sum of the limits, so this is going to be equal to, I'll do this first part in red, the limit as delta x approaches zero of, let's see I can rewrite this as cosine of x times sine of delta x over delta x plus the limit as delta x approaches zero of, and let's see I can factor out a sine of x here, so it's times sine of x, I factor that out and I'll be left with a cosine of delta x minus one, all of that over delta x, so that's this limit, and let's see if I can simplify this even more. Let me scroll down a bit. So this left hand expression I can rewrite, this cosine of x has nothing to do with the limit as delta x approaches zero, so we can actually take that outside of the limit. So we have the cosine of x times the limit as delta x approaches zero of sine of delta x over delta x, and now we need to add this thing, and let's see how I could write this.