Trig derivatives/anti-derivatives

• February 10th 2009, 12:17 PM
jschlarb
Trig derivatives/anti-derivatives
I have this function:

$v'=cos(2x)$

and I'm told that

$v=[sin(2x)]/2$

Does that mean if I have a trig function, say

$f= [sin(5x)]/5$

then
$f'=cos(5x)$?

or if

$g=[cos(5x)]/5$
then
$g'=-sin(5x)$?
• February 10th 2009, 01:34 PM
Jameson
Yes, all those statements are true. When integrating trig functions with a coefficient, you divide by this number to cancel out the extra coefficient when taking the derivative and using the chain rule.