## lovesit2x 2 years ago Find dx/dy for the following function: y=sinx+5e^.4x dx/dy =

1. Hoa

is it dx/dy?

2. lovesit2x

what does dx/dy equals

3. Hoa

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

4. Hoa

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

5. mathsmind

it will behave implicitly

6. mathsmind

i think she means dy/dx

7. lovesit2x

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

8. Hoa

@mathsmind you help her, ok?

9. mathsmind

no u help her

10. mathsmind

can u double check the question plz

11. mathsmind

it must be dy/dx at ur level

12. lovesit2x

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

13. mathsmind

ok

14. mathsmind

u allowed everyone to escape from this question hehehehe

15. lovesit2x

lol i know, i wish i could escape it too

16. Xavier

dx/dy = 1/(dy/dx)

17. lovesit2x

18. mathsmind

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

19. mathsmind

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

20. mathsmind

and y will become 1 when u differentiate it

21. lovesit2x

ok

22. Xavier

Just find dy/dx and take the reciprocal.

23. mathsmind

nope don't do that

24. mathsmind

they are not the same

25. Xavier

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

26. mathsmind

no it does not work like that

27. Xavier

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

28. mathsmind

look multiply both sides

29. mathsmind

u r missing the chain rule this is calculus not algebra

30. Xavier
31. mathsmind

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

32. Azteck

Can't you implicit differentiate in this situation?

33. Azteck

implicitly*

34. mathsmind

yes that is different from ur fomula

35. lovesit2x

im even more confused...

36. mathsmind

he wants u to use L rule

37. mathsmind

which is similar to what i said about the chain rule

38. mathsmind

Lebenz derived a formula from the chain rule

39. Azteck

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

40. mathsmind

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. mathsmind

because calculus is about functions and expansions

42. mathsmind

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. mathsmind

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

44. mathsmind

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

45. mathsmind

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

46. mathsmind

so take the inverse of the function then use the rule

47. mathsmind

or solve it implicitly as i started

48. mathsmind

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

49. mathsmind

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

50. mathsmind

the method u use is solving this in an implicit way

51. mathsmind

take dx/dy as a common factor

52. mathsmind

well @Xavier ur method also works congratulation!

53. mathsmind

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. mathsmind

works*

55. mathsmind

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