`"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that "`
`f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2))`.

Explanation

To prove that \( f'(x) = 3x^2 + 2x(a^2 + b^2 + c^2) \) for the function defined by the determinant:

\[
f(x) = \left| \begin{array}{ccc}
x + a^2 & ab & ac \\
ab & x + b^2 & bc \\
ac & bc & x + c^2
\end{array} \right|
...