Solve cos(x) = -sin(x)

Step-by-step solution

1. Cosine is one of the fundamental derivatives to memorise.

2. Geometric proof from the unit circle: as the angle increases by $dx$, the cosine coordinate decreases by $\sin(x)\,dx$.

3. Therefore: $\frac{d}{dx}\cos(x) = -\sin(x)$.

4. Note the negative sign — this is the most common error in introductory calculus.