Derivatives of Sums
Example:
f(x) = 4*x - sqrt(3*x-1)
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:
| f(x) |
= |
( 4*x ) | - |
( sqrt(3*x-1) ) |
The Derivative Rule for Sums:
The derivative of a sum is the sum of the derivatives.
If
then the derivative of
z is
| |
z' |
= |
( f(x) |
+ |
g(x) )' |
| |
|
= |
f '(x) |
+ |
g'(x) |
So our example,
| f(x) |
= |
( 4*x ) | - |
( sqrt(3*x-1) ) |
we can think of as
So the derivative is
| f '(x) |
= ( |
g(x) |
- |
h(x) |
)' |
| |
= |
g '(x) |
- |
h '(x) |
|
| |
= |
( 4*x) ' |
- |
( sqrt(3*x-1)) ' |
|
and we just need to know each of the derivatives on the right-hand
side of the equation. In this case these are
so the finished derivative is
| f '(x) |
= |
4 |
- |
3*(1/2)*(3*x-1)-1/2 (-1)*x-2 |
|
| |
= |
4 + (3/2)*x-2 (3*x-1)-1/2 |
![[]](/images/boxby.gif)
additional explanation for the derivative of sums
see another derivative of sums example
practice gateway test
previous page
Page Generated: Mon Jan 26 21:38:49 2026
Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose,
University of Michigan Math Dept.