Derivative of Cotangent Function/Corollary 2
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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
- 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $5$. Differential Calculus: Appendix: Derivatives of fundamental functions: $3.$ Trigonometric functions