If `f(x),g(x)a n dh(x)` are three polynomial of degree 2, then 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.

"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)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) 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))

phi(x)=f(x)*g(x)" and f'(x)*g'(x)=k ,then (2k)/(f(x)*g(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)

int(f(x)*g'(x)-f'(x)g(x))/(f(x)*g(x)){log g(x)-log f(x)}dx

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}