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lovesit2x

  • 2 years ago

Find dx/dy for the following function: y=sinx+5e^.4x dx/dy =

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  1. Hoa
    • 2 years ago
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    is it dx/dy?

  2. lovesit2x
    • 2 years ago
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    what does dx/dy equals

  3. Hoa
    • 2 years ago
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    I just want to make sure the question, because dx/ dy !=dy/dx

  4. Hoa
    • 2 years ago
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    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
    • 2 years ago
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    it will behave implicitly

  6. mathsmind
    • 2 years ago
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    i think she means dy/dx

  7. lovesit2x
    • 2 years ago
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    i thought i had to find the derivative and then solve for y

  8. Hoa
    • 2 years ago
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    @mathsmind you help her, ok?

  9. mathsmind
    • 2 years ago
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    no u help her

  10. mathsmind
    • 2 years ago
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    can u double check the question plz

  11. mathsmind
    • 2 years ago
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    it must be dy/dx at ur level

  12. lovesit2x
    • 2 years ago
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    \[Find \frac{ dx }{ dy } for the following function. Y = sinx + 5e ^{0.4x}\]

  13. mathsmind
    • 2 years ago
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    ok

  14. mathsmind
    • 2 years ago
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    u allowed everyone to escape from this question hehehehe

  15. lovesit2x
    • 2 years ago
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    lol i know, i wish i could escape it too

  16. Xavier
    • 2 years ago
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    dx/dy = 1/(dy/dx)

  17. lovesit2x
    • 2 years ago
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    @jim_thompson5910 rescue me please

  18. mathsmind
    • 2 years ago
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    ok i will solve it all it is implicit differentiation but in terms of x

  19. mathsmind
    • 2 years ago
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    so when u diff sin(x) it will be cos(x)dx/dy

  20. mathsmind
    • 2 years ago
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    and y will become 1 when u differentiate it

  21. lovesit2x
    • 2 years ago
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    ok

  22. Xavier
    • 2 years ago
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    Just find dy/dx and take the reciprocal.

  23. mathsmind
    • 2 years ago
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    nope don't do that

  24. mathsmind
    • 2 years ago
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    they are not the same

  25. Xavier
    • 2 years ago
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    Look, dx/dy = 1/(dy/dx)

  26. mathsmind
    • 2 years ago
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    no it does not work like that

  27. Xavier
    • 2 years ago
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    I hope you're kidding. I'm not manipulating fractions

  28. mathsmind
    • 2 years ago
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    look multiply both sides

  29. mathsmind
    • 2 years ago
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    u r missing the chain rule this is calculus not algebra

  30. Xavier
    • 2 years ago
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    http://math.stackexchange.com/questions/292590/is-dx-dy-1-dy-dx-in-calculus

  31. mathsmind
    • 2 years ago
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    the case where u use a reciprocal is by using the chain rule and cancelling each term out

  32. Azteck
    • 2 years ago
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    Can't you implicit differentiate in this situation?

  33. Azteck
    • 2 years ago
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    implicitly*

  34. mathsmind
    • 2 years ago
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    yes that is different from ur fomula

  35. lovesit2x
    • 2 years ago
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    im even more confused...

  36. mathsmind
    • 2 years ago
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    he wants u to use L rule

  37. mathsmind
    • 2 years ago
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    which is similar to what i said about the chain rule

  38. mathsmind
    • 2 years ago
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    Lebenz derived a formula from the chain rule

  39. Azteck
    • 2 years ago
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    \[\large y=\sin x+5e^{0.4x}\] \[\large 1=(\cos x +2e^{0.4x})\frac{dx}{dy}\]

  40. mathsmind
    • 2 years ago
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    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
    • 2 years ago
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    because calculus is about functions and expansions

  42. mathsmind
    • 2 years ago
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    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
    • 2 years ago
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    in other words ur Lebenz works if x= sin(y)+5e^y

  44. mathsmind
    • 2 years ago
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    so u can take the inverse of the function then apply the rule ok

  45. mathsmind
    • 2 years ago
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    i told u they are not the same but thanks anyway for bribing the topic up

  46. mathsmind
    • 2 years ago
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    so take the inverse of the function then use the rule

  47. mathsmind
    • 2 years ago
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    or solve it implicitly as i started

  48. mathsmind
    • 2 years ago
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    if the case was simple like this then implicit differentiation would have never exist

  49. mathsmind
    • 2 years ago
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    \[y = \sin(x) + e^{0.4x} \longrightarrow 1=\frac{dx}{dy}\cos(x)+2\frac{dx}{dy}e^{0.4x}\]

  50. mathsmind
    • 2 years ago
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    the method u use is solving this in an implicit way

  51. mathsmind
    • 2 years ago
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    take dx/dy as a common factor

  52. mathsmind
    • 2 years ago
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    well @Xavier ur method also works congratulation!

  53. mathsmind
    • 2 years ago
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    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
    • 2 years ago
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    works*

  55. mathsmind
    • 2 years ago
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    not just that i will change my proof for Kepler's laws of motion ...

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