Derivative of Cotangent Function/Corollary 1
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Corollary to Derivative of Cotangent Function
- $\map {\dfrac \d {\d x} } {\cot a x} = -a \csc^2 a x$
Proof
\(\ds \map {\dfrac \d {\d x} } {\cot x}\) | \(=\) | \(\ds -\csc^2 x\) | Derivative of $\cot x$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \map {\dfrac \d {\d x} } {\cot a x}\) | \(=\) | \(\ds -a \csc^2 a x\) | Derivative of Function of Constant Multiple |
$\blacksquare$