What is the derivative of $sin (x/2)$ ?

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Answer 1 · 2016-08-01T23:10:41

$1/2cos(x/2)$

We use the chain rule, as we have $y(u(x))$

$(dy)/(dx) = (dy)/(du)(du)/(dx)$

$u = x/2 implies (du)/(dx) = 1/2$

$y = sin(u) implies (dy)/(du) = cos(u)$

$therefore (dy)/(dx) = cos(u)*1/2 = 1/2cos(x/2)$

What is the derivative of sin (x/2) sin (x/2)?