Derivative of Cosine Function/Proof 1

Theorem

 * $D_x \left({\cos x}\right) = -\sin x$

Proof
From the definition of the cosine function, we have:
 * $\displaystyle \cos x = \sum_{n \mathop = 0}^\infty \left({-1}\right)^n \frac {x^{2n}}{\left({2n}\right)!}$

Then:

The result follows from the definition of the sine function.