(a) State clearly the Sum Rule, Difference Rule and Constant Multiple Rule for differentiation.
(b) Using the definition of the derivative, show that if c is a constant and f(x) is differentiable at x, then dxd[cf(x)]=cf′(x).
(c) Give one worked numerical example that illustrates the simultaneous use of all three rules in part (a) for differentiating a single function.