If fx-n x n n- 2 cos x cos n- 2 4 sin x sin n- 2 8 then find the value of d n dx n fx x-0 for all n- Z-

Given #160; f(x)=n x ^ n amp; n! amp; 2 cos x #160; amp; cosn π #160; 2 #160; #160; amp; 4 sin x #160; amp; sin nπ ...

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Adjoint of a Matrix

If fx=n x n...

Question

If $f (x) = n ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{n} & n! & 2 cos x & cos \frac{n π}{2} & 4 sin x & sin \frac{n π}{2} & 8 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣$ then find the value of ${(\frac{d^{n}}{{d x}^{n}} f (x))}_{x = 0} f o r a l l (n \in Z)$ .

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\frac{d^{n}}{d x^{n}} [f (x)] a t x = 1

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\frac{d^{n}}{d x^{n}} f (x)

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