Linearity of differentiation
This property of the
derivative, follows from the
sum rule in differentiation and the
constant factor rule in differentiation. Thus we can say that the act of differentiation
linear, or the
differential operator is a
linear operator.
Let f and g be functions. Now consider:
By the
sum rule in differentiation, this is:
By the
constant factor rule in differentiation, this reduces to:
Hence we have:
Omitting the brackets, this is often written as: