Derivatives of Basic Functions
At some point we just have to memorize the derivatives of functions.
This is the case with any function that is "elementary" -- that
is, not part of a combination with another function. Such functions
include things like sin(x), cos(x), csc(x), and
so on. A list of some of the most common of these, with their
derivatives, is given by the following.
The Derivative of Basic Functions:
| |
( e x )' |
= |
e x
|
| |
( a x )' |
= |
ln(a)
a x
|
| |
( sin(x) )' |
= |
cos(x)
|
| |
( cos(x) )' |
= |
-sin(x)
|
| |
( ln(x) )' |
= |
1 / x
|
|
|
| |
(xn) ' |
= |
n xn - 1
|
| |
( tan(x) )' |
= |
1 / ( cos(x) )2
|
| |
( arctan(x) )' |
= |
1 / ( 1 + x2 )
|
| |
( arcsin(x) )' |
= |
1 / sqrt( 1 - x2 )
|
| |
( arccos(x) )' |
= |
-1 / sqrt( 1 - x2 )
|
|
(cunning note: you can work out the derivative of
tan(x) using the
quotient
rule, and the derivatives of the inverse trig functions arcsine,
arccosine, etc., with implicit differentiation.)
Do we have to memorize these? Basically, yes. But that's not so
bad. In the long run, it will save you a lot of time and effort to
know these by heart.
![[]](images/boxby.gif)
practice gateway test
previous
page
Deriv Tutorials: Basic Functions
Last Modified: Tue May 1 14:48:06 EDT 2001
Comments to
glarose@umich.edu
©2001 Gavin LaRose, UM Math Dept.