## krypton Group Title inverse and inverse trignometric functions find d/dx(arctan^2(sqrt(x)) one year ago one year ago

1. hsmt Group Title

hi krypton.. you still there? I think i might be able to help if you are

2. krypton Group Title

yea dear

3. hsmt Group Title

consider the derivative of arctan^2(u) where u=sqrt x and use the chain rule...

4. hsmt Group Title

sorry. let's start with the derivative of (tan-1u)^2. what is the derivative of this little beastie. lol there we go...

5. krypton Group Title

u mean?

6. hsmt Group Title

what is the derivative of (f(x))^2?

7. hsmt Group Title

it would be something like 2(f(x))times f prime of x

8. hsmt Group Title

in this case, f(u)=tan-1u, where u=sqrt of x. does this make sense?

9. hsmt Group Title

questions are good here. the more you ask, the more i can help... :)

10. krypton Group Title

yea

11. hsmt Group Title

so what is the derivative of tan-1u?

12. hsmt Group Title

you can give me your best guess if you like

13. krypton Group Title

hmm actually i wasnt in the class when the topic was taught, but i thinkis =1/srt 1-x^2?

14. krypton Group Title

sorry 1/1+x^2

15. hsmt Group Title

that is totally correct. :) now replace the x with u so that we can use the chain rule where u=1/sqrtx.

16. krypton Group Title

17. hsmt Group Title

no, we have a power of tan-1. so the answer is 2(tan-1(sqrtx))(1/(1+x))1/2sqrtx

18. hsmt Group Title

is that making sense to you?

19. hsmt Group Title

still there?

20. krypton Group Title

ok

21. krypton Group Title

so what will be my final answer?

22. hsmt Group Title

it is above

23. krypton Group Title

can u help me with one other questionÉ

24. hsmt Group Title

if i can, i would be happy to

25. krypton Group Title

find $find d/dx (\sqrt{1-x ^{2}}+1/2\cos ^{-1}(x) and verify whether or \not this is equal \to (2x+1)d/dx \sin ^{-1}(-x)$

26. hsmt Group Title

ok. any ideas where to start?

27. hsmt Group Title

oh... and i didnt get anything beyond the arrow... sorry... but i think i have enough to figure it out. :)

28. krypton Group Title

hmm i dont have an idea

29. hsmt Group Title

ok, well, it is a rather large function, but it is a quotient (hint). So where might we start with this lovely little thing?

30. krypton Group Title

hmm..no idea lol

31. krypton Group Title

dont know anytin about the topic yet

32. hsmt Group Title

it is ok... remember the quotient rule d(f/g)/dx=[(fprime)g-(gprime)f]/g^2?

33. hsmt Group Title

in this case the numerator is f=sqrt(1-x^2) +1 and g=2cos-1(x)

34. hsmt Group Title

do you know the product rule?

35. krypton Group Title

yes

36. hsmt Group Title

phew...!! i am so glad. i thought for a sec we were outta options. lol

37. hsmt Group Title

ok

38. hsmt Group Title

look at f(x)=sqrt(1-x^2)+1 and g(x)=(2cos-1(x))^-1. does this make sense?

39. krypton Group Title

hahaha i can still remember my calculus 1, this calculus 2

40. krypton Group Title

yes it does

41. hsmt Group Title

glad to hear it... calc I is totally needed here... good, it makes sense. now we need fprime and gprime and i think you are pretty much homefree. so what is fprime and what is gprime?

42. hsmt Group Title

just algebra after you get the derivatives.

43. krypton Group Title

so i should get the derivative of each of them separatelyÉ