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5. Determine the derivative of each of the following functions. 1

6. Answer for Square 1 Home 1 a)4e x/4 b) e (x^3 + x^2) x (3x 2 + 2x)

7. 2 Determine the first and second derivatives of the following function.

8. Home 2 2 f ´ (x) = (7x 6 )(e (x^7) ) + 2xe (x^2) f ´´ (x) = (42x 5 )(e (x^7) ) + (49x 12 )(e (x^7) ) + 2e (x^2) + (4x 2 )(e (x^2) )

9. 3 Evaluate the derivative of the function at the given value of x. f(x) = e^2x + e^(x^2) at x = 2

10. Home 3 3 6e^4

11. 4 Determine the derivative of each of the following functions: 4 a)y = 7^8x b) y = 10 ^ ((x-1)^2) a) y = 6 ^ ((x^2) + x – 2)

12. Home 4 a)y ´ = 8ln7(7^8x) b)y ´ = (2x-2)(ln10)(10^((x-1)^2) c)y ´ = (2x+1)(ln6)(6^((x^2) + x – 2)

13. 5 5 Determine the equation of the line tangent to the function at the given value of x. f(x) = (2x)(4^(x^2)) at x=1

14. Home 5 5 f(x) = (8+16ln4)x – 16ln4

15. 6 6 Find a value of t such that f ´ (t)=0, if it exists. f(t) = 2te^ 8t

16. Answer for Square 6 Home 6 6 t = -1/8

17. 7 A radioactive substance decays exponentially over time. The amount of the substance that remains, P, after t years is given by P(t) = 100e -5t, where P is given as a percent. 7 a)Determine the equation of the rate of change of the function b)When 50% of the original sample has decayed, what is the rate of decay ?

18. Home 7 7 a)P ´ (t) = -500e -5t b)P ´ (1.059) = -2.5

19. 8 A drug is injected into the body in such a way that the concentration, C, in the blood at time t hours is given by the function C(t) = 10e -2t - e -3t. At what time does the highest concentration occur within the first 5h? 8

20. Home 8 During the first five hours, the highest concentration occurs at about 0.41 hours. 8

21. 9 Given f(x) = e -x cos2x, find f’’(0).

22. Answer for Square 9 Home 9. Because, then is not even. Because, then is not odd. Therefore is neither. c). Therefore, is even. d). Therefore, is even.