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

Suppose f and g are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all x and f^(prime) and g' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x)) is equal (a) (-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c) (-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

Suppose f and g are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all x and f^(prime) and g' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x)) is equal (a) (-2f^(prime)(x))/f (b) (-2g^(prime)(x))/(g(x)) (c) (-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

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))

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))

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))

Let f(x)a n dg(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) .

Let f(x)a n dg(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