The sum rule for differentiation states
![d/(dx)[f(x)+g(x)]=f^'(x)+g^'(x),](/images/equations/SumRule/NumberedEquation1.svg) |
(1)
|
where 
denotes a derivative and 
and 
are the derivatives of 
and 
,
respectively.
Given real-valued functions 
and 
that are continuous on the closed
interval ![[a,b]](/images/equations/SumRule/Inline8.svg)
, sum rule for definite integration
states,
![int_a^b[f(x)+g(x)]dx=int_a^bf(x)dx+int_a^bg(x)dx.](/images/equations/SumRule/NumberedEquation2.svg) |
(2)
|
Similarly, the sum rule for indefinite integration states,
![int[f(x)+g(x)]dx=intf(x)dx+intg(x)dx.](/images/equations/SumRule/NumberedEquation3.svg) |
(3)
|
