If `f_r(x),g_r(x),h_r(x),r=1,2,3` are polynomials such that `f_r(a)=g_r(a)=h_r(a),r=1,2,3a n d` `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^(prime)(x)a tx=a` is____________________

If f_r(x),g_r(x),h_r(x),r=1,2,3 are polynomials 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^(prime)(x) at x=a is____________________

If f_r(x),g_r(x),h_r(x),r=1,2,3 are polynomials 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^(prime)(x) at x=a is____________________

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) 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)]]

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) 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)):}| Find F.(x) at x=a

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_(x),h_(2)(x),h_(3)(x))| , then F'(x) at x=a is

If f_(n)(x),g_(n)(x),h_(n)(x),n=1, 2, 3 are polynomials in x such that f_(n)(a)=g_(n)(a)=h_(n)(a),n=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' (a) is equal to

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 ..... .

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 ..... .

If f_r(x),g_r(x),h_r(x),r=1,2,3 are differentiable function and y=|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))| then dy/dx= |(f\'_1(x), g\'_1(x), h\'_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))|+ |(f_1(x), g_1(x), h_1(x)), (f\'_2(x), g\'_2(x), h\'_2(x)),(f_3(x), g_3(x), h_3(x))|+|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f\'_3(x), g\'_3(x), h\'_3(x))| On the basis of above information, answer the following question: Let f(x)=|(x^4, cosx, sinx),(24, 0, 1),(a, a^2, a^3)| , where a is a constant Then at x= pi/2, d^4/dx^4{f(x)} is (A) 0 (B) a (C) a+a^3 (D) a+a^4

If f, g : R to R such that f(x) = 3 x^(2) - 2, g (x) = sin (2x) the g of =