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If f(x) =|{:(x^(n),,n!,,2),(cos x,,cos....

If `f(x) =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2),,8):}|,` then find the value of
`(d^(n))/(dx^(n)) [f(x)]_(x=0) .(n in z).`

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