[" 12.If "f(x)" and "g(x)" are polynomial functions of "x" ,then "],[" domain of "(f(x))/(g(x))" is "]

If f(x) and g(f) are two differentiable functions and g(x)!=0, then show trht (f(x))/(g(x)) is also differentiable (d)/(dx){(f(x))/(g(x))}=(g(x)(d)/(pi){f(x)}-g(x)(d)/(x){g(x)})/([g(x)]^(2))

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

If f(x) , g(x) and h(x) are polynomials of degree 2 , 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 :

If f and g are derivable function of x such that g'(a)ne0,g(a)=b" and "f(g(x))=x," then 'f'(b)=

If (x-1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of (a) f(x)g(x) (b) -f\ (x)+\ g(x) (c) f(x)-g(x) (d) {f(x)+g(x)}g(x)

If f(x) and g(x) are be two functions with all real numbers as their domains, then h(x) =[f(x) + f(-x)][g(x)-g(-x)] is:

If f(x), g(x) and h(x) are three polynomials 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.