ta123 4 years ago need help with the attachment

1. ta123

2. YTheManifold

a) Just plug in 1 for the numerator and g(x) for the denominator in the quotient rule. b) $-{\frac {1+k{{\rm e}^{s}}}{ \left( s+k{{\rm e}^{s}} \right) ^{2}}}$ assuming y is a function of s. c) Follows from $x^{-n} = \frac{1}{x^n}$ and $\frac{d}{dx} x^n = nx^{n-1}$

3. ta123

is the quotient rule the same thing as the reciprocal part b?

4. YTheManifold

What do you mean? The reciprocal rule is a special case of the quotient rule. You can use either one for part b, but it's easier to use the reciprocal rule.

5. ta123

The quotient rule f'g-fg'/g^(2)

6. ta123

but g(x) is just a variable

7. ta123

ok I got it

8. YTheManifold

What is your question? g is not just a variable, it's a function.

9. YTheManifold

10. ta123

OK I need help with differentiating the bottom on part could you show me step by step how to differentiate that one?

11. ta123

part b

12. ta123

and also the numerator of the function

13. YTheManifold

You need to differentiate$\Large s+k\cdot e^s$ with respect to s.

14. YTheManifold

The derivative of a sum is the sum of derivatives, so differentiate s and then differentiate k*e^s.

15. YTheManifold

What is the derivative of s?

16. raheen

17. ta123

1

18. YTheManifold

Yes. And what is the derivative of e^s ?

19. raheen

@ta, see the attachee

20. ta123

e^(s)

21. YTheManifold

22. YTheManifold

Yes, so now you can add them together and you get the derivative

23. YTheManifold

And then just plug that into the formula in part a)

24. ta123

1+e^(s)

25. YTheManifold

No! Don't forget the factor k!

26. YTheManifold

k does not depend on s, so you can just leave it unchanged

27. YTheManifold

But you must not forget it :D

28. raheen

29. raheen

here u r

30. YTheManifold

raheen there is still no explanation of part b :D

31. raheen

32. raheen

part b asking to find using the rule only

33. YTheManifold

ta123 do you have more questions?

34. raheen

whears the other 2 parts are to prove

35. raheen

@ta got that?

36. YTheManifold

lol raheen are you just trying to get a medal, because I can give you one if thats what you want :D

37. ta123

38. raheen

no YThe, I always try to help , pls don read the things in wrong way

39. YTheManifold

40. ta123

yes, thanks for the help Y and raheen

41. raheen

ta why some ppl are using an offensive words?

42. raheen

I think I stayed with u b4 more than 2 hrs, without any annyance, right?

43. ta123

yes

44. raheen

thank u.

45. ta123

no prob!