Pre-Calc Homework Solutions 119

Pre-Calc Homework Solutions 119 - Chapter 3 Review dy dx d...

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Unformatted text preview: Chapter 3 Review dy dx d 1 ln x) (e dx d ln (sin x) dx d 1 ln x (e e ) dx d (ex) dx 119 15. e cot x, for Alternate solution, using logarithmic differentiation: y ln y ln y (2x)2x x2 1 dy 16. dx 1 d (sin x) sin x dx cos x sin x values of x in the intervals (k , (k dr 17. dx 1) ), where k is even. ln (2x) ln 2 ln (2x) ln x ln x2 1 d 1 d ln (cos 1 x) cos 1 x dx cos 1 x dx 1 1 1 cos 1 x 1 x2 cos 1x 1 x 2 d log2 ( 2) d d log5 (t dt 2 18. 19. dr d ds dt 1 d 2 ( ) ln 2 d 1 d (t 7) ln 5 dt 2 2 ln 2 2 ln 2 1 , 7) ln 5 7) (t 7) (t d ln y dx 1 dy y dx dy dx dy dx 1 ln (x 2 1) 2 1 d [ln 2 ln x x ln 2 ln (x 2 1)] 2 dx 1 1 1 0 ln 2 (2x) x 2 x2 1 1 x y ln 2 x x2 1 (2x)2x 1 x ln 2 x2 1 x2 1 x x ln 2 t ds 20. dt 7 23. d (8 t ) dt d 8 (ln 8) ( t) dt t dy dx dy du d tan 1x e dx d sin 1 du 1 1 1 u2 2 ( 1 1 1 e tan 1 x d dx tan 1 x etan x 1 x2 1 8 t ln 8 24. 1 u2 d u 2)2 du u2 21. Use logarithmic differentiation. y ln y ln y d ln y dx 1 dy y dx dy dx dy dx dy 22. dx d dx x2 x ln x 1 u2 u u 1 u2 ln (x ln x) (ln x)(ln x) d (ln x)2 dx d 2 ln x ln x dx 2y ln x x 2x ln x ln x x (2x)2x x2 1 d (2x)(2x) dx d 1 dx [(2x)2x] ( 2u) 25. dy dt d (t sec 1 t dt 1 ln t) 2 (t) t t t t2 1 t2 1 1 (sec sec 1 1 t)(1) 1 2t t 1 2t 26. dy dt d [(1 dt t 2) cot t 2) 1 1 2t] (cot 1 (1 2 1 1 1 2 x2 1 1 (2) (2t)2 2t)(2t) x2 2t 2 4t 2 2t cot 1 1 2t z 2) 1 x2 x2 1[(2x)(2x)(ln 2) 27. (2x) 1 (2x)(2)] x2 1 (2x)(2x) dy dz (z) d (z cos 1 z dz 1 1 z 1 z2 z2 (cos 1 z)(1) 2 z 1 z2 1 1 z2 ( 2z) cos z (x 2 1)(2 )(2x ln 2 2) (x 2 1)3/2 1)(x ln 2 (x 2 1)3/2 2 x 2x (2 ) dy dx 2 x cos 28. d (2 dx 1 z x 1 csc 1) x 1 1 (2 2x)[(x 2 1) x 2] x) 1 ( x) 1 2 (2 2 )(x ln 2 x x ln 2 (x 2 1)3/2 (2 2x)(x 3 ln 2 x ln 2 (x 2 1)3/2 1) x 3 1 x ) 2 (2 x (2 csc x ( 1 x x)2 1 1 2 x x) 1 2 x csc 1 1 1 1 x 1 x x x csc x 1 ...
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