Question

If y=tan^2x, show that d^2y/d^2x=2(1+y(1+3y)

Answer 1

y = tan^2x
arctan(√y) = x
1/(1+y) * 1/2√y y' = 1
y' = 2√y (y+1)
y" = (1/√y (y+1) + 2√y)y'
= 1/√y (y+1+2y) * 2√y (y+1)
= 2(1+3y)(y+1)