derivative of 𝑦 = csch 𝜃 (1 − ln csch 𝜃)

asked by guest
on Dec 30, 2024 at 3:18 pm



You asked:

Find the derivative of the function y=csch(θ)(1ln(csch(θ)))y = \operatorname{csch}\left( θ \right) \left(1 - \ln\left( \operatorname{csch}\left( θ \right) \right)\right) with respect to θθ.

MathBot Answer:

dydθ=(1log(csch(θ)))coth(θ)csch(θ)+coth(θ)csch(θ)\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)}