How do I a differentiate a cosine function?

The differential is the slope of the graph at any point. So if we imagine a cosine in our heads, it starts at a peak and goes down to a negative peak. So in terms of the gradient (or slope) it starts at 0 and goes negative.A sine graph starts at 0 and goes positive, however our gradient goes negative. To fix this we simply invert everything or times by -1.Hence the differential of a cosine function is equal to the negative of a sine function.