Derivatives of Sums
Example:
y = sin(t) - (tan(t))3/8
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 |
= |
( sin(t) ) | - |
( (tan(t))3/8 ) |
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 |
= |
( sin(t) ) | - |
( (tan(t))3/8 ) |
we can think of as
So the derivative is
| y ' |
= ( |
f(t) |
- |
g(t) |
)' |
| |
= |
f '(t) |
- |
g '(t) |
|
| |
= |
( sin(t)) ' |
- |
( (tan(t))3/8) ' |
|
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 ' |
= |
cos(t) |
- |
(3/8)*(tan(t))-5/8 (1 / (cos(t))2) |
|
| |
= |
cos(t) - (3/8)*(tan(t))-5/8 (1 / (cos(t))2) |
![[]](/images/boxby.gif)
additional explanation for the derivative of sums
see another derivative of sums example
practice gateway test
previous page
Page Generated: Wed Nov 26 06:52:53 2025
Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose,
University of Michigan Math Dept.