Let `f` be a differentiable function satisfying the relation `f(xy) = xf(y) + yf(x)- 2xy` (where `x, y gt 0`) and `f'(1) = 3,` then

Let f be a differentiable function satisfying the relation f(xy)=xf(y)+yf(x)−2xy .(where x, y >0) and f ′ (1)=3, then find f(x)

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

Let f(x) be a differentiable function satisfying the condition f((x)/(y)) = (f(x))/(f(y)) , where y != 0, f(y) != 0 for all x,y y in R and f'(1) = 2 The value of underset(-1)overset(1)(int) f(x) dx is

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: RrarrR satisfies the equation f(x) f(y) - f(xy) = x+ y, AAx,y in R and f(1) gt 0 , then

Let f(x) be a differentiable function which satisfies the equation f(xy)=f(x)+f(y) for all x>0,y>0 then f'(x) equals to