derivatives)of)trigonometric)functions) definitions:) · lesson& &...
Post on 28-Jun-2020
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Lesson&&
Derivatives)of)Trigonometric)Functions)&Definitions:)!!" !"#$ = !!"#$& & & & !
!" !"#$ = −!"#$&&&Now&find&the&derivative&of&tan(x)&using&the&previous&two&definitions.&&&&&&&&&&&Definition:&&&&& !!" !"#$ =&&More)trig)definitions:)
!!" !"#$ = −!"!!!& & & & !
!" !"#$ = sec(!)tan(!)&&!!" !"!# = − csc ! cot(!)&
&Remember:)&&Example:&Find&the&derivative.&&!!!!! ! = 5!"#$ − 7!"#$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&! ! = !!cos!&&&&&
Lesson&&Example:&Find&!
!!!!!&&&when&&!! = !"#$ + !"#$!!!!!!!!!!!!!!!!!!!!!!!!!!!&
&&&&&&&Example:&Find&the&derivative&and&simplify.&
! ! = csc!(!)tan!(!)&
&&&&&Example:&Find&the&derivative.&&
ℎ ! = cos!(!)!"#$(!)&
&&&&&&&You&try:&Find&the&equation&of&the&tangent&line&when&! = ! !!&
! ! = 4!"#$%&!$&&&&&
Lesson&
&
The$Chain$Rule$!!" !(! ! ) = !′(! ! ) ∙ !′(!)&
Example:&! = 2(6!! − 2)!"&
&&&&&&&You&try:&!!!ℎ ! = 5(3!! + 4!)!&&&Example:&Find&the&derivative.&
! = !"!!!&&&&&&&&&Example:&Find&the&derivative.&
! = 3!tan!(5!!)&&&&&&&&&
Lesson&
&
You&try:&!!!!! ! = !"#!(!!!)! &
&&Example:&
! ! = sin!(!"#2!)&&&&&&Example:&
x ( )f x ( )f x! ( )g x ( )g x! 1 6 4 2 5 2 9 5 3 8 3 10 -4 4 2 4 -1 3 6 7
&Let&&ℎ ! = ! ! ! .!!!!Find&ℎ! 2 .!&&&&&&&Let&! ! = ! ! .!!!!Find&!! 4 .&&&&&&&Let&! ! = ! 4!! .!!!!Find&!! 1 .&&&&
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