A function fff satisfies f(x+y)=f(x)f(y)f(x+y) = f(x)f(y)f(x+y)=f(x)f(y) for all x,yx,yx,y. If f(0)=1f(0) = 1f(0)=1 and f′(0)=kf'(0) = kf′(0)=k, determine f′(x)f'(x)f′(x).
f'(x) = kf(x)
f'(x) = f(x)
f'(x) = kx
f'(x) = f(x) + k