Derivatives of Sums, Differences, and Constant Multiples - Expii

To differentiate linear combinations of functions, some helpful rules are: (f+g)'=f'+g' for differentiable functions f and g (derivative of sum); (f-g)'=f'-g' for differentiable functions f and g (derivative of difference); and (cf)'=cf' for a differentiable function f and a constant c (derivative of constant multiple). These rules apply whether you are thinking of derivatives at a point (numbers) or derivatives on an interval (functions).