The Eighth Gate
Arriving at the eighth and penultimate gate, you immediately get to work. \"Computer, translate this gate for me.\"
Your computer replies with the follow:
The function $f(t) = a \left(\sin \left(t^8\right)\right)^6$ models the position of an oscillating particle that has recently been
discovered. Assume that $a$ is a constant. What is the function that represents the velocity of this particle?
Note: If you want to write a power of a trigonometric function, remember that writing $\sin(x)$ to the fourth power
as $\sin^4(x)$ is just a shorthand method. To be mathematically correct, you should write that as $(\sin(x))^4$,
which is what your computer expects and can translate
Velocity Function:
