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

`if =|{:(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

AI Generated Solution

To solve the problem, we need to evaluate the determinant given by: \[ f(x) = \begin{vmatrix} x^n & n! & 2 \\ \cos x & \cos\left(\frac{n\pi}{2}\right) & 4 \\ \sin x & \sin\left(\frac{n\pi}{2}\right) & 8 \end{vmatrix} ...
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