Derivative of Hyperbolic Tangent of a x
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Theorem
- $\map {\dfrac \d {\d x} } {\tanh a x} = a \sech^2 a x$
Proof
\(\ds \map {\dfrac \d {\d x} } {\tanh x}\) | \(=\) | \(\ds \sech^2 x\) | Derivative of $\tanh x$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \map {\dfrac \d {\d x} } {\tanh a x}\) | \(=\) | \(\ds a \sech^2 a x\) | Derivative of Function of Constant Multiple |
$\blacksquare$