calculus help please? thanx?

Question

what is the derivative of this equation s(t)=sec√t

Answer 1

Use the chain rule, which states that (f(g(x)))' = f'(g(x))*g'(x). The inner function (g) is sqrt(t) and the outer function (f) is sec(t). Note that the derivative of sqrt(t) is 1 / (2*sqrt(t)) and the derivative of sec(t) is sec(t)*tan(t).

Answer 2

If you set Θ = √t, then
s = sec Θ
By the chain rule, ds/dt = (ds/dΘ)(dΘ/dt)
dΘ/dt = ½t^(-½)
ds/dΘ = secΘtanΘ

Now ds/dt = (secΘtanΘ)*(½t^(-½))
Substitute t back in for theta:
ds/dt = [sec(√t)tan(√t)]*(½t^(-½))