A function `f:RtoR` is such that `f(x+y)=f(x).f(y)` for all x.y` inR` and `f(x)ne0` for all `x inR`. If `f'(0)=2` then `f'(x)` is equal to

A function f: RvecR satisfies the equation f(x+y)=f(x)f(y) for all x , y in Ra n df(x)!=0fora l lx in Rdot If f(x) is differentiable at x=0a n df^(prime)(0)=2, then prove that f^(prime)(x)=2f(x)dot

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to

Let f be a differentiable function from R to R such that abs(f(x)-f(y))abs(le2)abs(x-y)^(3//2) ,for all x,y inR .If f(0)=1 ,then int_(0)^(1)f^2(x)dx is equal to

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

If for a function f : R to R f (x +y ) =F(x ) + f(y) for all x and y then f(0) is

Let f:R to R be a function satisfying f(x+y)=f(x)=lambdaxy+3x^(2)y^(2)"for all "x,y in R If f(3)=4 and f(5)=52, then f'(x) is equal to

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

If f(2x+3y, 2x-7y)=20x, then f(x,y) equals :