Detailed process is required

1. Consider the following function, f(a) = sin if x + 0 if x = 0 (a) (3 marks) Prove that the function f is differentiable at x = 0 using the definition of derivatives. (b) (2 marks) Find the formula of the derivative, f' (x) for x # 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. Note: after this work, you may want to see if the derivative function is continuous at x = 0. While the original function f is differentiable and so also continuous at x = 0, its derivative is not continuous at x = 0