## anonymous 3 years ago Help me find the derivative of this function

1. anonymous

$\huge A(t)= 20\sin^2(\frac{ t }{ 1000\pi })$

2. bahrom7893

Use power + chain rules

3. bahrom7893

This is a very straightforward question.

4. anonymous

|dw:1371609626141:dw|

5. anonymous

like that?

6. bahrom7893

you forgot the final chain rule

7. anonymous

|dw:1371609898205:dw|

8. anonymous

@bahrom7893 what do you mean?

9. bahrom7893

|dw:1371610057029:dw|

10. anonymous

|dw:1371610058623:dw|

11. anonymous

@bahrom7893 wait i dont get it tho, why the extra fraction :S

12. bahrom7893

derivative of |dw:1371610223598:dw|

13. bahrom7893

|dw:1371610328327:dw|

14. anonymous

|dw:1371610801029:dw| @bahrom7893

15. bahrom7893

Noooo

16. anonymous

|dw:1371610749100:dw|

17. bahrom7893

Guys stop confusing him. Burhan, your first answer was right. You just forgot to add in that fraction.

18. anonymous

How do i simplify further ?

19. bahrom7893

just use algebra, cancel out some fractions.

20. anonymous

howww im really confused !!

21. anonymous

The answer key says it should be $\huge A'(t) = \frac{ 1 }{ 50\pi }\sin (\frac{ t }{ 50\pi })$

22. anonymous

@bahrom7893

23. bahrom7893

2Sin(x)Cos(x) = ? (double angle formula)

24. anonymous

if i just simplify that fraction to 'x' then =20((2sinx)(cosx)(x)) =20(xsinx)

25. anonymous

.just use what I gave if you're still confused....

26. bahrom7893

|dw:1371612098284:dw|

27. bahrom7893

so according to our calculations, the answer should be: |dw:1371612290008:dw| which seemed right. the book might have a typo

28. anonymous

........which is what I said 40 minutes ago........ |dw:1371612421231:dw|

29. bahrom7893

lol

30. anonymous

thanks both !@bahrom7893 @primeralph

31. anonymous

You're very welcome.

32. bahrom7893

np my friend :)

33. anonymous

b) What is the first value of t greater than 0 for which the derivative is equal to 0?

34. anonymous

@primeralph

35. bahrom7893

set the derivative equal to 0, then check the signs nearby

36. anonymous

@primeralph what does that mean ^ ?

37. anonymous

for it to equal zero, you have to shift t by the period pi

38. anonymous

|dw:1371615489438:dw|