Find the derivative of f(t) = csch t (1-ln csch t)

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to use the product rule to find the derivative of f(t) such that:

`f'(t) = (cosech t)'(1 - ln cosech t) + (cosech t)(1 - ln cosech t)'`

`f'(t) = cosech t*cotanh t*(1 - ln cosech t) + (cosech t)(-(cosech t)')/(cosech t)`

`f'(t) = cosech t*cotanh t*(1 - ln cosech t) - cosech t*cotanh t`

You need to factor out `cosech t*cotanh t`  such that:

`f'(t) = cosech t*cotanh t(1 - ln cosech t - 1)`

`f'(t) = -cosech t*cotanh*ln cosech t`

Hence, evaluating the derivative of the given function yields `f'(t) = -cosech t*cotanh*ln cosech t` .