What is the derivative of cos(x)?

The correct answer to this question is − sin x. To solve this, one would need to know about many facts that come from trigonometry. The first fact they must know is that cos( A + B) = cos A cos B − sin A sin B.

One must also know the fundamental trigonometry fact which is lim θ → 0 sin θ θ = 1 lim θ → 0 cos θ −1 θ = 0. After knowing this, one would use these two facts to solve the derivative. A student that studies math would be more likely asked this question.