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

`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).`

Text Solution

Verified by Experts

The correct Answer is:
0
`(d^(n))/(dx^(n))[f(x)]=|{:((d^(n))/(dx^(n))(x^(n)),n!,2),((d^(n))/(dx^(n))(cos x),cos (npi)/(2),4),((d^(n))/(dx^(n))(sin x), sin (npi)/(2),8):}|`
`=|{:(n!,n!,2),(cos(x+(npi)/(2)),cos""(npi)/(2),4),(sin(x+(npi)/(2)),sin""(npi)/(2),8):}|`
`"or "(d^(n))/(dx^(n))[f(x)]_(x=0)=0`
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