Find ds/dt.........calculus?

Question

Find ds/dt if x=sec z and z=t^2+1. Express the answer in terms of t.

Details please

Answer 1

Feel that question should give:-
s = sec z and z = t² + 1
ds/dz = secz. tanz
dz/dt = 2t
ds/dt = sec z.tan z.2t
ds / dt = sec (t² + 1).tan (t² + 1). 2t

Answer 2

First of all, get a TI-89....

Second of all this is an identity. plug in t^2+1 for Z.

the question now reads find ds/dt of sec( t^2+1)

Integrate sec(t^2+1) in terms of t. Use an online derivative finder if you don't have a TI calculator. Or look up the integration of the secant function, usually in the back of a calc book.

Answer 3

I don't give you a fish. I teach you how to fish...
for ds/dt you should find a function (y=f(x)) which s is y and t is x.
it means you should find a function like: s=f(t).
then you should calculate differential of function s.

but you don't have any s here.
if you meant z here is the answer:

dz/dt = 2t