Pre-Calc Homework Solutions 116

Pre-Calc Homework Solutions 116 - 116 dy dx dy dx dy dx dy...

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Unformatted text preview: 116 dy dx dy dx dy dx dy dx dy dx dy dx Section 3.9 d (x ) dx d 1 (x dx d x dx d 1 e x dx d x 8 dx d 9 x dx d csc x 3 dx 2) 1 11. 12. 13. 14. 15. 16. 17. x 25. 2)x 1 2 1 dy dx dy dx d ln (x dx 2) 1 x d (x 2 dx 1 2) 1 x 2 ,x 2 2 (1 2x (1 e)x 1 (1 2)x 2 26. 2 2 1 d ln (2x 2) dx 1 ,x 1 x 1 d ln (2 dx sin x 2 cos x d ln (x 2 dx 2x d (2x 2 dx 2) 2x 2 e 1 (1 e)x e 27. dy dx cos x) 2 1 d (2 cos x dx cos x) 8x ln 8 28. 9 x (ln 9) ( x) d dx d dx dy dx 1) 1 x2 d 2 (x 1 dx 1 ln x 1 x 1 x 1) 2x x2 1 9 x ln 9 29. 30. dy dx d ln (ln x) dx dy dx d (x ln x dx 1 d ln x ln x dx 1 x ln x 3csc x (ln 3) (csc x) 3csc x (ln 3)( csc x cot x) 3csc x (ln 3)(csc x cot x) x) ln x (x) (ln x)(1) 1 1 31. dy dx ln x 1 18. dy dx d cot x 3 dx 3 cot x d (ln 3) (cot x) dx 3cot x (ln 3)( csc 2 x) 3cot x (ln 3)(csc 2x) 19. Use logarithmic differentiation. y ln y ln y d (ln y) dx 1 dy y dx dy dx dy dx dy 32. dx d d ln x 2 (log4 x 2) dx dx ln 4 1 2 2 1 ln 4 x x ln 4 x ln 2 d d ln x 1/2 (log5 x) dx dx ln 5 1 1 d 1 (ln x) 2 ln 5 dx 2 ln 5 x d log2 (3x dx 3 ,x (3x 1) ln 2 d dx 2 (ln x) ln 4 x ln x ln x ln x ln x ln x d (ln x)2 dx 1 (2 ln x) x 2y ln x x 2x ln x ln x x ln x d 2 dx ln 5 1 ,x 2x ln 5 1 d (3x 1) ln 2 dx 1 0 1) 33. dy dx 1) 1 3 (3x 34. dy dx 1 d d log10 (x 1)1/2 log10 (x 1) 2 dx dx 1 1 d 1 (x 1) ,x 2 (x 1) ln 10 dx 2(x 1) ln 10 1 d log2 x dx d ( log2 x) dx 1 ,x x ln 2 1 0 35. 36. dy dx dy dx 20. Use logarithmic differentiation. y ln y ln y ln y y dy dx x 1/ln x ln x 1/ln x 1 ln x ln x d 1 1 d (log2 x) dx log2 x (log2 x)2 dx 1 1 1 or (log2 x)2 x ln 2 x(ln 2)(log2 x)2 d (ln 2 log2 x) dx 1 1 (ln 2) ,x x x ln 2 ln 2 x(ln x)2 37. dy dx (ln 2) (log2 x) 0 x ln 3) d dx 1 e d (e) dx d ln (x 2) dx d (ln x)2 dx d ln (x 1) dx 10 d ln x dx 38. 0, x 0 1 (2x) x2 2 ln x x 1 ,x x 2 x dy dx d 1 d log3 (1 x ln 3) (1 dx (1 x ln 3) ln 3 dx ln 3 1 1 ,x (1 x ln 3) ln 3 1 x ln 3 ln 3 d (log10 e x) dx 1 ln 10 d (x log10 e) dx 21. 22. 23. 24. dy dx dy dx dy dx dy dx 1 d 2 (x ) x 2 dx 39. dy dx log10 e ln e ln 10 2 ln x d (ln x) dx d ( ln x) dx d (ln 10 dx 0 1 x 1 ,x x 40. dy dx d ln 10x dx d (x ln 10) dx ln 10 ln x) 0 0 ...
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