This is just a type of composite function, but here goes.

10sin(πt/15)(π/15);

2π/3 (sin(πt/15))

edit*

I'm sorry, I guess that was a bit vague.

You take the derivative of the first part, multiply that times the second part. Add that to the first part times the derivative of the second part. Okay, not such a good explanation. Look;

d/dt -10 = 0, because it is a constant.

d/dt cos(πt/15) = -sin(πt/15) (π/15), the second part was a composite function.

Now you have, if you can follow the bumbling above;

(0)(cos[πt/15] + -10(-sin[πt/15])(π/15);

0 + 10sin(πt/15)(π/15) = (2π/3)sin(πt/15)

Sorry, if that is still a bad explanation, I am not a teacher at all.