If-f-x-x-2-4x-sin-4x-find-f-6-x-

Question Number 199176 by cortano12 last updated on 29/Oct/23

If f (x) = (x^{2} - 4 x) \sin 4 x

find f^{(6)} (x) .

Answered by MM42 last updated on 29/Oct/23

f = u . v

\Rightarrow f^{(n)} = \underset{i = 0}{\sum^{n}} (\begin{matrix} n \\ i \end{matrix}) \times u^{(n - i)} \times v^{(i)}

l e t : u = x^{2} - 4 x & v = s i n 4 x

\Rightarrow f^{(6)} (x) = 30 \times 4^{4} s i n 4 x + 6 \times 4^{5} \times (2 x - 4) c o s 4 x - 4^{6} \times (x^{2} - 4 x) s i n 4 x ✓

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