Derivative of Cosine Function/Proof 3

$D_x \left({\cos x}\right) = -\sin x$
 $\displaystyle D_x \cos x$ $=$ $\displaystyle D_x \, \map \sin {\frac \pi 2 - x}$ Sine of Complement equals Cosine $\displaystyle$ $=$ $\displaystyle -\map \cos {\frac \pi 2 - x}$ Derivative of Sine Function and Chain Rule $\displaystyle$ $=$ $\displaystyle -\sin x$ Cosine of Complement equals Sine
$\blacksquare$