help me with all of these derivative questions?

Question

Please tell me if the expression below are true or false and why??

1.the 100th derivative of sinh x is coshx
2.the function tanh x is odd, that is, tanh(-x) = -tanh x
3.the only functions whose fourth derivatives are equal to cos t are
of the form cos t + C, where C is any constant.
4.if y satisfies the equation y^2 + xy - 1 = 0, then dy/dx exists every
where
5.if the derivative of f(g(x)) is equal to the derivative of f(x) for all x,
then g(x) = x for all x

Answer 1

1. false. odd derivatives of sinh x are equal to cosh x, even ones are equal to sinh x.
2. true. tahn x=sinh x / cosh x, sinh x is odd, coshx is even, odd / even is odd.
3. false. cos t + any cubic polynomial has 4th derivative cos t.
4. true. the expression for dy/dx is undefined when x+2y=0, but there are no such points on the curve that satisfies the original equation, because that would mean y^2=-1.
5. false. For example, let g(x)=x+2*pi, and let f(x)=sin(x). Then f(g(x))=f(x), so their derivatives are equal too, but g(x) is not x.

Answer 2

1) The first derivative is cosh x.
The second derivative is sinh x
Odd numbered derivatives will be cosh x and even numbered derivatives will be sinh x
#1 is false.

Answer 3

All of them are true