Derivatives of Sums

Example:

y = 2^x + (3)²

The first thing to notice when finding the derivative of this function is that it is the sum of several terms, as shown in color below:

( 2^x )

( (3)² )

The Derivative Rule for Sums:

The derivative of a sum is the sum of the derivatives.
If

( f(x)

g(x) )

then the derivative of z is

	z'	=	( f(x)	+	g(x) )'
		=	f '(x)	+	g'(x)

So our example,

( 2^x )

( (3)² )

we can think of as

f(x)

g(x)

So the derivative is

and we just need to know each of the derivatives on the right-hand side of the equation. In this case these are

( 2^x )'	=	(ln(2))*2^x	(by the derivative rules for basic functions)
( (3)² )'	=	0	(by the derivative rule for constants)

so the finished derivative is

y '	=	(ln(2))*2^x	+	0
	=	(ln(2))*2^x

Page Generated: Mon Jan 19 14:08:15 2026
Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose, University of Michigan Math Dept.