## anonymous 3 years ago Find dx/dy for the following function: y=sinx+5e^.4x dx/dy =

1. anonymous

is it dx/dy?

2. anonymous

what does dx/dy equals

3. anonymous

I just want to make sure the question, because dx/ dy !=dy/dx

4. anonymous

if it is dx/ dy. it's not easy to solve. you must solve for x first , then take derivative respect to y.

5. anonymous

it will behave implicitly

6. anonymous

i think she means dy/dx

7. anonymous

i thought i had to find the derivative and then solve for y

8. anonymous

@mathsmind you help her, ok?

9. anonymous

no u help her

10. anonymous

can u double check the question plz

11. anonymous

it must be dy/dx at ur level

12. anonymous

$Find \frac{ dx }{ dy } for the following function. Y = sinx + 5e ^{0.4x}$

13. anonymous

ok

14. anonymous

u allowed everyone to escape from this question hehehehe

15. anonymous

lol i know, i wish i could escape it too

16. anonymous

dx/dy = 1/(dy/dx)

17. anonymous

18. anonymous

ok i will solve it all it is implicit differentiation but in terms of x

19. anonymous

so when u diff sin(x) it will be cos(x)dx/dy

20. anonymous

and y will become 1 when u differentiate it

21. anonymous

ok

22. anonymous

Just find dy/dx and take the reciprocal.

23. anonymous

nope don't do that

24. anonymous

they are not the same

25. anonymous

Look, dx/dy = 1/(dy/dx)

26. anonymous

no it does not work like that

27. anonymous

I hope you're kidding. I'm not manipulating fractions

28. anonymous

look multiply both sides

29. anonymous

u r missing the chain rule this is calculus not algebra

30. anonymous
31. anonymous

the case where u use a reciprocal is by using the chain rule and cancelling each term out

32. anonymous

Can't you implicit differentiate in this situation?

33. anonymous

implicitly*

34. anonymous

yes that is different from ur fomula

35. anonymous

im even more confused...

36. anonymous

he wants u to use L rule

37. anonymous

which is similar to what i said about the chain rule

38. anonymous

Lebenz derived a formula from the chain rule

39. anonymous

$\large y=\sin x+5e^{0.4x}$ $\large 1=(\cos x +2e^{0.4x})\frac{dx}{dy}$

40. anonymous

nope i told u don't do that, unless if u want to apply Lebenz rule u need to take the inverse of the function then take the reciprocal ...

41. anonymous

because calculus is about functions and expansions

42. anonymous

read that carefully If the derivative of y = f(x) is dy/dx, then the derivative of the inverse function which expresses x in terms of y is given by the formula

43. anonymous

in other words ur Lebenz works if x= sin(y)+5e^y

44. anonymous

so u can take the inverse of the function then apply the rule ok

45. anonymous

i told u they are not the same but thanks anyway for bribing the topic up

46. anonymous

so take the inverse of the function then use the rule

47. anonymous

or solve it implicitly as i started

48. anonymous

if the case was simple like this then implicit differentiation would have never exist

49. anonymous

$y = \sin(x) + e^{0.4x} \longrightarrow 1=\frac{dx}{dy}\cos(x)+2\frac{dx}{dy}e^{0.4x}$

50. anonymous

the method u use is solving this in an implicit way

51. anonymous

take dx/dy as a common factor

52. anonymous

well @Xavier ur method also works congratulation!

53. anonymous

so both methods work fine, actually u made me come with a new theory in math, or a different proof for Leben'z formula. although maths is not my major, but i will write a new paper on this and publish it

54. anonymous

works*

55. anonymous

not just that i will change my proof for Kepler's laws of motion ...