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If f(r)(x), g(r)(x), h(r) (x), r=1, 2, ...

If `f_(r)(x), g_(r)(x), h_(r) (x), r=1, 2, 3` are polynomials in x such that ` f_(r)(a) = g_(r)(a) = h_(r) (a), r=1, 2, 3`
`and " "F(x) =|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}|`
then F'(x) at x = a is ..... .

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The correct Answer is:
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Given, `F(x)=|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}|`
`:." "F'(x)=|{:(f_(1)'(x)" "f_(2)'(x)" "f_(3)'(x)),(g_(1)(x)" "g_(2)(x)" " g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}| +|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)'(x)" "g_(2)'(x)" "g_(3)'(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x) ):}|+|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)'(x)" "h_(2)'(x)" " h_(3)'(x)):}|`
`rArr" "F'(a) = 0+0+0=0`
`[:' f_(r)(a) = g_(r)(a) = h_(r) (a) , r=1,2,3]`
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