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 If F(x)=det[[f',g,hf',g',h'f'',g'',h'']] then F'(x) is

If f(x),g(x) andh (x) are three polynomial of degree 2, then prove that f(x)g(x)h(x)f'(x)g'(xh'(x)f''(x)g''(x)h''(x)| is a constant polynomial.

If f(x) g(x) and h(x) are three polynomials of degree 2 and Delta = |( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))| then Delta(x) is a polynomial of degree (dashes denote the differentiation).

If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f^(prime)(x)g^(prime)(x)h^(prime)(x)f^(x)g^(x)h^(x)|i sacon s t a n tpol y nom i a l

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)=|x-1|" and "g(x)=f(f(f(x))) , then for xgt2,g'(x) 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,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(xg)'(x h)'(x^(f2)f)' '(x^2g)' '(x^2h)' '| prove that ^(prime)=|fgff'g' h '(x^3f' ')'(x^3g' ')'(x^3h ' ')'|

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)