Derivative of cos(x)

Differentiating cos(x) is a single-rule problem: everything follows from the trigonometric derivatives. That makes it a good expression for isolating and practicing that one technique.

The trigonometric derivatives follow the standard cycle: sine differentiates to cosine, cosine to negative sine, and tangent to secant squared. The sign on the cosine derivative is a frequent source of errors, so it is worth double-checking.

A good way to verify a derivative by hand is to compare it against the step-by-step breakdown above — each step names the rule being applied, so you can pinpoint exactly where your own work diverges if the answers differ.