Section 3.8 : Derivatives of Hyperbolic Functions
2. Differentiate \(R\left( t \right) = \tan \left( t \right) + {t^2}{\mathop{\rm csch}\nolimits} \left( t \right)\).
Show SolutionNot much to do here other than take the derivative using the formulas from class.
\[\require{bbox} \bbox[2pt,border:1px solid black]{{R'\left( t \right) = {{\sec }^2}\left( t \right) + 2t{\mathop{\rm csch}\nolimits} \left( t \right) - {t^2}{\mathop{\rm csch}\nolimits} \left( t \right)\coth \left( t \right)}}\]