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 $f(t)=a(sin(t^{10}){)}^6$ 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?