If `f(x), h(x)` are polynomials of degree 4 and `|(f(x), g(x),h(x)),(a, b, c),(p,q,r)|``=mx^4+nx^3+rx^2+sx+r` be an identity in x, then `|(f''(0) - f''(0),g''(0) - g''(0),h''(0) -h''(0)),(a,b,c),(p,q,r)|` is

If f(x), g(x), h(x) are polynomials in x of degree 2 If F(x)=|[f,g,h],[f',g',h'],[ f'', g'', h'' ]| then F'(x) is

If f(x),g(x),h(x) are polynomials in x of degree 2 If F(x)=det[[f',g,hf',g',h'f'',g'',h'']] then F'(x) is

If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h 'f' 'g' ' h ' '| , then F^(prime)(x) is equal to 1 (b) 0 (c) -1 (d) f(x)dotg(x)doth(x)

If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h 'f' 'g' ' h ' '| , then F^(prime)(x) is equal to 1 (b) 0 (c) -1 (d) f(x)dotg(x)doth(x)

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))

Let F(x) = f(x).g(x).h(x) x in R , where f(x) , g(x) & h(x) are differentiable function. At some point x_0, F'(x_0) = 21 F(x_0) , f'(x_0) = 4f(x_0),g'(x_0) = -7g(x_0), h'(x_0)= k.h(x_0) then k/4 =

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(x)=(g(x))+(g(-x))/2+2/([h(x)+h(-x)]^(-1)) where g and h are differentiable functions then f'(0)