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) 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.

"Prove that "phi(x)=|{:(f(x),g(x),h(x)),(f'(x),g'(x),h'(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), 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 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 y=|f(x)g(x)h(x)lmnabc|, prove that (dy)/(dx)=|f'(x)g'(x)h'(x)lmnabc|

Let y=f(x),y=g(x),y=h(x) be three invertible functions defined from R rarr R Then y=f(x)+g(x)+h(x) is