Derivative of Cosine Function/Proof 3
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Theorem
- $\map {\dfrac \d {\d x} } {\cos x} = -\sin x$
Proof
| \(\ds \frac \d {\d x} \cos x\) | \(=\) | \(\ds \frac \d {\d x} \map \sin {\frac \pi 2 - x}\) | 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 |
$\blacksquare$