Aim: How do we prepare for the log and exponential differentiation and integration exam? dy
I. Find dx 3
1. y = ln(−14x ) 4. y = ln(ln(cos x)) 5
2. y = (ln 2x) y = ln 4
x 2 +1
x 2 −1 3. y = ln(4 − x 2 ) 6. y = e
−4 x+4
5. 2
x
8. y = xe − e 9. y = 4
x π
11. y = π x 4
xy
2
12. x + e − y = 20 2x
3
7. y = 2e 2
10. y = log 3 (x − 2) 2 x−1
Aim: How do we prepare for the log and exponential differentiation and integration exam? 13. ln y + xy + 8x = 25 14. Write the equation of the tangent line of y = 8x 2 + ln(3x + 1) + 1 at x=0 II. Find the integral or definite integral of the given function 1
7x
8x 3 − 7x 2 −1
dx
dx
dx
∫
∫ 2
∫
2x
15. 5 − x 16. x − 8 17. Aim: How do we prepare for the log and exponential differentiation and integration exam? (ln x)3
∫ 2x dx
(e 4 x + e)dx
2e x (1+ e x )4 dx
18. 19. ∫
20. ∫
e x + e− x
∫ x − x dx
π ecos x sin x dx
(e x − e− x )2 dx
21. e − e
22. ∫
23. ∫
4
e2
e x
2
∫ 2 x dx
∫ x dx
24. 1
25. 1
Aim: How do we prepare for the log and exponential differentiation and integration exam? −x
26. Find relative extrema and inflection points of y = xe . Justify your answers.