# Derivative of Cosine Function/Proof 3

$\map {\dfrac \d {\d x} } {\cos x} = -\sin x$
 $\ds \frac \d {\d x} \cos x$ $=$ $\ds \frac \d {\d x} \map \sin {\frac \pi 2 - x}$ Sine of Complement equals Cosine $\ds$ $=$ $\ds -\map \cos {\frac \pi 2 - x}$ Derivative of Sine Function and Chain Rule for Derivatives $\ds$ $=$ $\ds -\sin x$ Cosine of Complement equals Sine
$\blacksquare$