Question

more calc help.
find first and 2econd derivatives with respect to x
x = 2sect, y = tant, t = pi/3

Answer 1

dx/dt = 2sec(t)tan(t)
dy/dt = sec^2(t)

Answer 2

dy/dx = (dy/dt * dt/dx) = sec^2(t) / 2sec^2(t)tan(t)
= sec(t)/2tan(t) = (csc(t)/2)

Answer 3

(d^2y/dx^2) = -(csc(t)cot(t))/2 (t=pi/3) = 1/sqrt(3)

Answer 4

could someone check my work?