1.

Recall that

, which follows from the definition of the hyperbolic functions:

so by the chain rule, the derivative reduces to

2.

The derivative on the left side follows from the same principle as in the first problem. Solving for

, you get

3.

Product rule:

then power (for the first derivative) and chain rules:


This can be reduced a bit more, but you can stop here since this is one of the answer choices.
4.

Chain rule for both sides:


I would stop here, but maybe your answer choices are solutions for

explicitly. If that's the case, solving

is a purely algebraic exercise.