derivative of 𝑦 = csch 𝜃 (1 − ln csch 𝜃)
You asked:
Find the derivative of the function \(y = \operatorname{csch}\left( θ \right) \left(1 - \ln\left( \operatorname{csch}\left( θ \right) \right)\right)\) with respect to \(θ\).
MathBot Answer:
\[\frac{d y}{d θ} = - \left(1 - \log{\left(\operatorname{csch}{\left(θ \right)} \right)}\right) \coth{\left(θ \right)} \operatorname{csch}{\left(θ \right)} + \coth{\left(θ \right)} \operatorname{csch}{\left(θ \right)}\]