Lesson&#25&&

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&#1:&Find&the&derivative.&&!!!!! ! = 5!"#$ − 7!"#$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&! ! = !!cos!&&&&&

Lesson&#25&&Example&#2:&Find&!

!!!!!&&&when&&!! = !"#$ + !"#$!!!!!!!!!!!!!!!!!!!!!!!!!!!&

&&&&&&&Example&#3:&Find&the&derivative&and&simplify.&

! ! = csc!(!)tan!(!)&

&&&&&Example&#4:&Find&the&derivative.&&

ℎ ! = cos!(!)!"#$(!)&

&&&&&&&You&try:&Find&the&equation&of&the&tangent&line&when&! = ! !!&

! ! = 4!"#$%&!$&&&&&

Lesson&#26&

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The$Chain$Rule$!!" !(! ! ) = !′(! ! ) ∙ !′(!)&

Example&#1:&! = 2(6!! − 2)!"&

&&&&&&&You&try:&!!!ℎ ! = 5(3!! + 4!)!&&&Example&#2:&Find&the&derivative.&

! = !"!!!&&&&&&&&&Example&#3:&Find&the&derivative.&

! = 3!tan!(5!!)&&&&&&&&&

Lesson&#26&

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You&try:&!!!!! ! = !"#!(!!!)! &

&&Example&#4:&

! ! = sin!(!"#2!)&&&&&&Example&#5:&

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 .&&&&

Lesson&#26&

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AP&Test&Questions:&&

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