let-f-x-determinant-x-x-2-x-3-0-2x-3x-2-1-0-x-find-f-x-

Question Number 138167 by physicstutes last updated on 10/Apr/21

let f (x) = | \begin{matrix} x & x^{2} & x^{3} \\ 0 & 2 x & 3 x^{2} \\ 1 & 0 & x \end{matrix} | find

f^{'} (x)

Answered by Dwaipayan Shikari last updated on 10/Apr/21

f (x) = x (2 x^{2}) - x^{2} (- 3 x^{2}) + x^{3} (0 - 2 x)

= 2 x^{3} + 3 x^{4} - 2 x^{4} = 2 x^{3} + x^{4}

f^{'} (x) = 6 x^{2} + 4 x^{3}

Answered by mathmax by abdo last updated on 10/Apr/21

f (x) = x | \begin{matrix} 2 x {3 x}^{2} \\ 0 x \end{matrix} | - o + 1 | \begin{matrix} x^{2} x^{3} \\ 2 x {3 x}^{2} \end{matrix} |

= x ({2 x}^{2}) + ({3 x}^{4} - {2 x}^{4}) = x^{4} + {2 x}^{3} \Rightarrow f^{^{'}} (x) = {4 x}^{3} + {6 x}^{2}