Suppose f and g are functions having second derivatives `f' and g'` every where, if `f(x).g(x)=1` for all `x and f'', g''` are never zero then `(f''(x))/(f'(x))-(g'(x))/(g'(x))` equals

Suppose fa n dg are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all xa n df^(prime)a n dg' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x))e q u a l (a)(-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c)(-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

int{f(x)g'(x)-f'g(x)}dx equals

Let f(x) and g(x) be two function having finite nonzero third-order derivatives f''(x) and g''(x) for all x in R. If f(x)g(x)=1 for all x in R, then prove that (f''')/(f')-(g'')/(g')=3((f'')/(f)-(g'')/(g))

If f and g are two functions having derivative of order three for all x satisfying f(x)g(x)=C (constant) and (f''')/(f')-"A" (f'')/f -(g''')/(g')+(3g")/g=0 . Then A is equal to

Let f(x) and g(x) be real valued functions such that f(x)g(x)=1, AA x in R."If "f''(x) and g''(x)" exists"AA x in R and f'(x) and g'(x) are never zero, then prove that (f''(x))/(f'(x))-(g''(x))/(g'(x))=(2f'(x))/(f(x))

Let f(x) and g(x) be real valued functions such that f(x)g(x)=1, AA x in R."If "f''(x) and g''(x)" exists"AA x in R and f'(x) and g'(x) are never zero, then prove that (f''(x))/(f'(x))-(g''(x))/(g'(x))=(2f'(x))/(f(x))

Find an anti-derivative of the function f(x)g(x)-f(x)g(x)

If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2)=4=f'(2) then f''(24)+g''(24) is