A function `f:R->R` satisfies the differential equation `2xy+(1+x^2)y'=1` where `f(0)=0` then

" A function "f:R rarr R" satisfies the equation "f(x)f(y)-f(xy)=x+y" and "f(y)>0" ,then "f(x)f^(-1)(x)=

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for all x,y in R.f(x)!=0 Suppose that the function is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x)