Step 1 use the chain rule:

dy/dx=[1/(1+tan(x))](sec(x))^2

Step 2 use product rule (you could use the quotient ruleif you prefer)

and chain rule:

d^2y/dx^2=[1/(1+tan(x))^2](-1) [sec(x)]^4 + [1/(1+tan(x))].2.[sec(x)]^2 tan(x)

when x=0 tan(x)=0, and sec(x)=1, result follows.(i) Show that d2y/dx2 = -1 when x = 0.

RonL