If `f(x+y+z)=f(x) f(y) f(z) ne 0`for all x,y,z and f(2)=5, f'(0)=2, find f'(2).

If f(x+y+z)=f(x)f(y)f(z)ne0 , for all x, y, z and f(2)=4,f'(0)=3 , find f'(2) .

If f(x+y) = f(x) * f(y) for all real x and y and f(5)=2,f'(0) = 3 , find f'(5).

If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) will be

If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then find f(x).

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

If f(x+y)=f(x)+f(y) for all real x and y, show that f(x)=xf(1) .

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

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

A real valued function satisfies the relation f(x+y)=f(x)+f(y)+(e^x-1)(e^y-1) , AAx,y in R . If f'(0) = 2, find f(x).