find the dy/dx of s(t)= (4/3pi)sin3t+(4/5pi)cos5t

Answer 1

Just use the chain rule for each term

ds/dt = ds/du du/dt

u = 3t
du/dx = 3
s(u) = sin u
ds/du = cos u

So, ds/dt = (4/3π)(cos 3t)(3) + (4/5π)(-sin 5t)(5)
= 4/π cos 3t - 4/π sin 5t

Unless by 4/3π you mean 4/3 * π.