Derivative of Hyperbolic Cosine of a x
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Theorem
- $\map {\dfrac \d {\d x} } {\cosh a x} = a \sinh a x$
Proof
\(\ds \map {\dfrac \d {\d x} } {\cosh x}\) | \(=\) | \(\ds \sinh x\) | Derivative of $\cosh x$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \map {\dfrac \d {\d x} } {\cosh a x}\) | \(=\) | \(\ds a \sinh a x\) | Derivative of Function of Constant Multiple |
$\blacksquare$