Derivative of Hyperbolic Cosecant of a x
Jump to navigation
Jump to search
Theorem
- $\map {\dfrac \d {\d x} } {\csch a x} = -a \csch a x \coth a x$
Proof
\(\ds \map {\dfrac \d {\d x} } {\csch x}\) | \(=\) | \(\ds -\csch x \coth x\) | Derivative of $\csch x$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \map {\dfrac \d {\d x} } {\csch a x}\) | \(=\) | \(\ds -a \csch a x \coth a x\) | Derivative of Function of Constant Multiple |
$\blacksquare$