Chapter3: Differentiation x x dx d cos ) (sin x x dx d sin ) (cos x x dx d 2 sec ) (tan x x x dx d cot csc ) (csc x x x dx d tan sec ) (sec x x dx d 2 csc ) (cot DERIVATIVES OF TRIGONOMETRIC FUNCTIONS: ) ( ' ) ( ' ) ( ' x g x g f x H Chain Rule: Implicit diff. )) ( ( ' 1 ' ) ( 1 1 x f f x f a x g x g x g dx d a ln 1 ) ( ) ( ' ) ( log ) ( ) ( ' ) ( ln x g x g x g dx d x x x ' ) ( ' ) ( ) ( ) ( ' ) ( ) ( x g x f x g x f x g x f dx d Derivative Product Rule 2 )] ( [ ) ( ' ) ( ) ( ) ( ' ) ( ) ( x g x g x f x g x f x g x f dx d Derivative Quotient Rule Derivative of exponential ) (ln ) ( a a a dx d x x 0 a a x x f at dif ) ( a x x f at cont ) ( exist ) ( lim x f a x
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Chapter3: Differentiation
xxdx
dcos)(sin
xxdx
dsin)(cos
xxdx
d 2sec)(tan
xxxdx
dcotcsc)(csc
xxxdx
dtansec)(sec
xxdx
d 2csc)(cot
DERIVATIVES OF TRIGONOMETRIC FUNCTIONS:
)(')(')(' xgxgfxH Chain Rule:
Implicit diff.
))(('
1' )(
11
xffxf
axg
xgxg
dx
da ln
1
)(
)(')(log
)(
)(')(ln
xg
xgxg
dx
d
x
xx '
)(')()()(')()( xgxfxgxfxgxfdx
d
Derivative Product Rule
2)]([
)(')()()('
)(
)(
xg
xgxfxgxf
xg
xf
dx
d
Derivative Quotient Rule Derivative of exponential