The brightness of Delta Cephei increases and decreases according to its brightness function
B(t) = 4 + 0.35sin(2πt/b). The brightness of the star b is 5 days. How fast does its brightness changes at time equals one day?

Substitute the average brightness of the star 5 days into the brightness function,

   B(t) = 4 + 0.35 sin(2πt/5)

Let f(t) = 2πt/5, then

   B(t) = 4 + 0.35 sin(f(t))

Using the to Chain Rule,

the rate of changes for the brightness of Delta Cephei is

After a day the brightness is