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'''a n dg''' for all x in Rdot If f(x)g(x)=1 for all x in R , then prove that f'''(/)f^(prime)-g'''^(/)g^(prime)=3(f''^(/)f-g''^(/)g)dot

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

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

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 g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

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))

Let f(x) be polynomial function of defree 2 such that f(x)gt0 for all x in R. If g(x)=f(x)+f'(x)+f''(x) for all x, then

Let f(x)=sqrt(x) and g(x) = x be two functions defined over the set of nonnegative real numbers. Find (f + g) (x) , (f - g) (x) , (fg) (x) and (f/g)(x) .

Let f(x)=sqrt(x) and g(x) = x be two functions defined over the set of nonnegative real numbers. Find (f + g) (x) , (f g) (x) , (fg) (x) and (f/g)(x) .