Solve Derivative Problem

Question

Does anyone know how solve this problem step by step. It is a derivative problem (4/3 pi) sin3t (4/3 pi) sin5t

Answer 1

step1. Take out the 4/3 pi.  The final derivative will be multiplied by 16/9 pi^2

step 2.  Derivative of 2 functions (u and v)

(uv)' = u'v + uv'

d/dt of sin3t = 3cos3t

step 3: put it all together

((3 * cos3t * sin3t) + (5 * sin5t * cos5t)) * 16/9 pi^2

step 4: if there are any trig identities to make cos(x)sin(x) any simpler -- apply them.  I can't remember if there are, nor do I have time to look them up.

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