# tra08 - CALCULUS Trancedental Functions. Chain Rule (IV) 1....

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Unformatted text preview: CALCULUS Trancedental Functions. Chain Rule (IV) 1. Differentiate: f ( x ) = (sin x ) √ x 2. Differentiate: f ( x ) = (cos x ) cos x 3. Differentiate: f ( x ) = ( √ x ) x 4. Differentiate: f ( x ) = (ln x ) log x 5. Differentiate: f ( x ) = (cos x ) √ x 6. Differentiate: f ( x ) = ( √ x ) ln x 7. Differentiate: f ( x ) = ( √ x ) sin x 8. Differentiate: f ( x ) = (log x ) sin x 9. Differentiate: f ( x ) = (cos x ) sin x 10. Differentiate: f ( x ) = (ln x ) x A n s w e r s : 1 . f ( x ) = ( s in x ) √ x 1 2 √ x ln s in x + c o s x √ x s in x 2 . f ( x ) = ( c o s x ) c o s x [ ln c o s x + 1 ] (- s in x ) 3 . f ( x ) = ( √ x ) x ln √ x + 1 2 4 . f ( x ) = ( ln x ) l o g x 1 ( ln 1 ) x ln ln x + 1 x l o g x ln x 5 . f ( x ) = ( c o s x ) √ x 1 2 √ x ln c o s x + (- s in x ) √ x c o s x 6 . f ( x ) = ( √ x ) l n x 1 x ln √ x + ln x 2 x 7 . f ( x ) = ( √ x ) s i n x c o s x ln √ x + s in x 2 x 8 . f ( x ) = ( l o g x ) s i n x c o s x ln l o g x + 1 ( ln 1 ) x s in x l o g x 9 . f ( x ) = ( c o s x ) s i n x c o s x ln c o s x + (- s in x ) s in x c o s x 1 . f ( x ) = ( ln x ) x ln ln x + 1 ln x c 2009 La Citadelle 1 of 5 www.la-citadelle.com CALCULUS Trancedental Functions. Chain Rule (IV) Solutions: 1. f ( x ) = d d x f ( x ) = d d x (sin x ) √ x Write the original function as a power using the identity: f g = e g ln f f ( x ) = d d x e √ x ln sin x J Apply: d d x e f ( x ) = e f ( x ) d d x f ( x ) = e √ x ln sin x d d x √ x lnsin x J Apply: f g = e g ln f d d x f ( x ) g ( x ) = g ( x ) d d x f ( x ) + f ( x ) d d x g ( x ) = (sin x ) √ x lnsin x d d x √ x + √ x d d x lnsin x J Apply: d d x √ x = 1 2 √ x d d x ln f ( x ) = 1 f ( x ) f ( x ) = (sin x ) √ x 1 2 √ x lnsin x + √ x 1 sin x d d x sin x J Apply: d d x...
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## This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Fall '08 term at North Texas.

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tra08 - CALCULUS Trancedental Functions. Chain Rule (IV) 1....

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