Let f(x)=(1/2)π−(1/2)x (mod 2π) for all ∣x∣<2π g(x)=Σ_(k=1) ^∞ ((sin(kx))/k) , for all ∣x∣<2π f(x) and g(x) are identically equal function. 1)Even though f and g are equivalent functions why is the derivative of f well-defined while the derivative of g is not ?? 2) is it true that continuity implies differentiable?? Does differentiability imply continuity??