## lovesit2x Group Title Find dx/dy for the following function: y=sinx+5e^.4x dx/dy = one year ago one year ago

1. Hoa Group Title

is it dx/dy?

2. lovesit2x Group Title

what does dx/dy equals

3. Hoa Group Title

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

4. Hoa Group Title

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 Group Title

it will behave implicitly

6. mathsmind Group Title

i think she means dy/dx

7. lovesit2x Group Title

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

8. Hoa Group Title

@mathsmind you help her, ok?

9. mathsmind Group Title

no u help her

10. mathsmind Group Title

can u double check the question plz

11. mathsmind Group Title

it must be dy/dx at ur level

12. lovesit2x Group Title

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

13. mathsmind Group Title

ok

14. mathsmind Group Title

u allowed everyone to escape from this question hehehehe

15. lovesit2x Group Title

lol i know, i wish i could escape it too

16. Xavier Group Title

dx/dy = 1/(dy/dx)

17. lovesit2x Group Title

18. mathsmind Group Title

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

19. mathsmind Group Title

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

20. mathsmind Group Title

and y will become 1 when u differentiate it

21. lovesit2x Group Title

ok

22. Xavier Group Title

Just find dy/dx and take the reciprocal.

23. mathsmind Group Title

nope don't do that

24. mathsmind Group Title

they are not the same

25. Xavier Group Title

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

26. mathsmind Group Title

no it does not work like that

27. Xavier Group Title

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

28. mathsmind Group Title

look multiply both sides

29. mathsmind Group Title

u r missing the chain rule this is calculus not algebra

30. Xavier Group Title
31. mathsmind Group Title

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

32. Azteck Group Title

Can't you implicit differentiate in this situation?

33. Azteck Group Title

implicitly*

34. mathsmind Group Title

yes that is different from ur fomula

35. lovesit2x Group Title

im even more confused...

36. mathsmind Group Title

he wants u to use L rule

37. mathsmind Group Title

which is similar to what i said about the chain rule

38. mathsmind Group Title

Lebenz derived a formula from the chain rule

39. Azteck Group Title

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

40. mathsmind Group Title

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 Group Title

because calculus is about functions and expansions

42. mathsmind Group Title

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 Group Title

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

44. mathsmind Group Title

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

45. mathsmind Group Title

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

46. mathsmind Group Title

so take the inverse of the function then use the rule

47. mathsmind Group Title

or solve it implicitly as i started

48. mathsmind Group Title

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

49. mathsmind Group Title

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

50. mathsmind Group Title

the method u use is solving this in an implicit way

51. mathsmind Group Title

take dx/dy as a common factor

52. mathsmind Group Title

well @Xavier ur method also works congratulation!

53. mathsmind Group Title

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 Group Title

works*

55. mathsmind Group Title

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