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) is constant then f'(x) = g'(x)

f(x)= x, g(x)= (1)/(x) and h(x)= f(x) g(x). If h(x) = 1 then…….

If y= |(f(x),g(x),h(x)),(l,m,n),(a,b,c)| , prove that (dy)/(dx)= |(f'(x),g'(x),h'(x)),(l,m,n),(a,b,c)|

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

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) is a polynomial of degree n(gt2) and f(x)=f(alpha-x) , (where alpha is a fixed real number ), then the degree of f'(x) is

If f,g and h are differentiable functions of x and Delta = |{:(f , g , h), ((xf)' , (xg)' , (xh)'), ((x^(2) f)'' , (x^(2) g)'', (x^(2) h)''):}| then prove that Delta'=|{:(f , g , h), (f' , g' , h'), ((x^(3) f'')' , (x^(3) g'')', (x^(3) h)'')':}| .

If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then f(x)=0 has

If f(x)=sinx,g(x)=x^(2)andh(x)=logx. IF F(x)=h(f(g(x))), then F'(x) is