Final answer:
To find the derivative of the function f(t) = arccsc(-8t²), use the chain rule and the derivative of arccsc(u) is -1/(|u|sqrt(u²-1)).
Step-by-step explanation:
To find the derivative of the function f(t) = arccsc(-8t²), we can use the chain rule. The derivative of arccsc(u) is -1/(|u|sqrt(u²-1)), so we have:
f'(t) = -1/(|-8t²|sqrt((-8t²)²-1)) * (d/dt)(-8t²)
= -1/(8t²*sqrt((64t⁴)-1)) * (-16t)
= 2t/(t²*sqrt((64t⁴)-1)).