The Eighth Gate

Arriving at the eighth and penultimate gate, you immediately get to wark. "Computer, translate this gate for me$."$ Your computar replies with the follow:

The function $f(t)-a(sin(t^4){)}^6$ modols the position of an ascilating particie that has recently been discoversd. Assume that $a$ is a constant. What is the function that represents the velocity of this particie?

Note: If you want to write a powar of a trigonometric function, remember that writing sin$(x)$ to the fourth power as $si{n}^4(x)$ is just a shorthand method. To be mathematically carrect you should write that as $(sin(x){)}^4.$ which is what your compuler expects and can translate.

Valocity Function $$