y = arcsec(x), Find dy/dx.

The key to this problem is to apply sec to both sides, and then differentiate implicitly: sec(y)=x; dsec(y)/dx = 1; tan(y)sec(y)dy/dx = 1; dy/dx = 1/(tan(y)sec(y)). Then using the fact that sec(y)=x and tan²x + 1 = sec²x, we can rewrite our derivative in terms of x only: dy/dx = 1/(x√(x²-1))