Madasmaths very hard question

Prove that the differential of 1+coshx/1-coshx is equivalent to coth(x/2)Cosech^2(x/2)

Would very much appreciate if anyone could offer a solution or a way to start from the RHS for this question. Its question 4 of part 4 of his differentiation practice iii booklet.

All you need to do is differentiate $\dfrac{1+\cosh x}{1-\cosh x}$ and show that this result is the same as $\coth \dfrac{x}{2} \mathrm{cosech}^2 \dfrac{x}{2}$.

To differentate, you should employ the quotient rule. What do you get?

-2sinhxcoshx/(1-coshx)^2. Unsure of how to progress from that stage. From inspection i presumed multiplying through the LHS by 1+coshx would be whats required, but couldnt progress that way either.