Derivative of Cotangent Function/Corollary 2

From ProofWiki
Jump to navigation Jump to search

Corollary to Derivative of Cotangent Function

$\dfrac \d {\d x} \cot x = -1 - \cot^2 x$


Proof

\(\ds \dfrac \d {\d x} \cot x\) \(=\) \(\ds -\csc^2 x\) Derivative of $\cot x$
\(\ds \) \(=\) \(\ds -\paren {\cot^2 x + 1}\) Difference of Squares of Cosecant and Cotangent
\(\ds \) \(=\) \(\ds -1 - \cot^2 x\) rearranging

$\blacksquare$


Sources