Question

differentaite w.r to x
h(x) = arcosh(x^3 + 2).

Answer 1

I don't have the derivative of arcosh at the tip of my tongue , and would have to look it up.
I think you can probably do the same.

Answer 2

just as d/dx arccos(u) = -1/√(1-u^2) u',

d/dx arccosh(u) = 1/√(x^2-1) u'

so, in this case, you end up with

3x^2/√((x^3+2)^2 - 1)