Derivatives of Sums

The derivative of a sum is nice because it behaves as we expect. Once we recognize a function is a sum, say, something like x + cos(x), we apply the derivative rule for sums:

So we just have to find the derivatives of each term in the sum, and add them together. In our simple example, x + cos(x), this is easy: the derivatives of the terms are

term	derivative	why
x	1	derivative of a variable
cos(x)	-sin(x)	derivative of cosine

So the derivative works out as