Derivatives of Sums
Example:
y = tan(q) - (tan(q))1/8
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:
| y |
= |
( tan(q) ) | - |
( (tan(q))1/8 ) |
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,
| y |
= |
( tan(q) ) | - |
( (tan(q))1/8 ) |
we can think of as
So the derivative is
| y ' |
= ( |
f(q) |
- |
g(q) |
)' |
| |
= |
f '(q) |
- |
g '(q) |
|
| |
= |
( tan(q)) ' |
- |
( (tan(q))1/8) ' |
|
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
| y ' |
= |
1 / (cos(q))2 |
- |
(1/8)*(tan(q))-7/8 (1 / (cos(q))2) |
|
| |
= |
1 / (cos(q))2 - (1/8)*(tan(q))-7/8 (1 / (cos(q))2) |
![[]](/images/boxby.gif)
additional explanation for the derivative of sums
see another derivative of sums example
practice gateway test
previous page
Page Generated: Thu Jan 15 17:45:21 2026
Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose,
University of Michigan Math Dept.