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DLS

siny=xsin(a+y) dy/dx=?

  • one year ago
  • one year ago

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  1. DLS
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    I have a small doubt here..

    • one year ago
  2. DLS
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    is xsin(a+y) to be solved with product rule?

    • one year ago
  3. lgbasallote
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    dy/dx means you take the derivative of x... since sin(a+y) does not include any x in it... no, you don't use product rule. you treat sin(a+y) as a constant coefficient

    • one year ago
  4. DLS
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    :o?

    • one year ago
  5. hartnn
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    ummm.... u need to use product rule...

    • one year ago
  6. DLS
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    I did..

    • one year ago
  7. hartnn
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    because y is the function of x

    • one year ago
  8. DLS
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    What I want to ask is..if I had ysin(a+y) then I wuldve used chain rule?

    • one year ago
  9. lgbasallote
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    you only use product rule when two facots include x for example xsin x <-- x and sinx both have x so you use product rule xsiny <--- siny doesn't have x so treat it as coefficient remember that @hartnn ?

    • one year ago
  10. hartnn
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    no, product again, because both are functions of x

    • one year ago
  11. hartnn
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    sin y doesn't have x, right bu since y is the function of x....

    • one year ago
  12. hartnn
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    d/dx sin y = cos y dy/dx

    • one year ago
  13. DLS
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    ive done that only

    • one year ago
  14. DLS
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    but even WFA treats it as 0

    • one year ago
  15. hartnn
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    WFA ?

    • one year ago
  16. DLS
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    wolfaram :P ALPHA

    • one year ago
  17. DLS
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    spelling/*

    • one year ago
  18. hartnn
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    no...x sin(a+y) needs product rule.

    • one year ago
  19. DLS
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    :/

    • one year ago
  20. hartnn
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    x cos(a+y) dy/dx + sin(a+y)

    • one year ago
  21. hartnn
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    cos y dy/dx =x cos(a+y) dy/dx + sin(a+y) isolate dy/dx

    • one year ago
  22. hartnn
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    your WFA http://www.wolframalpha.com/input/?i=siny%3Dxsin%28a%2By%29%2C++dy%2Fdx%3D%3F

    • one year ago
  23. hartnn
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    it doesn't treat it as 0.

    • one year ago
  24. DLS
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    oh nvm :o

    • one year ago
  25. DLS
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    but still not clear why product rule..its used in product of 2 functions so x and sin(a+y) x is not a function,y is

    • one year ago
  26. hartnn
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    x is a function of x x^1

    • one year ago
  27. DLS
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    doesnt make any sense :S

    • one year ago
  28. DLS
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    every variable is afunction of itself then

    • one year ago
  29. hartnn
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    you can say that. f(x) = x^n with n=1.

    • one year ago
  30. DLS
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    why didnt we use chain rule for sin(a+y)

    • one year ago
  31. hartnn
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    we actually did.

    • one year ago
  32. DLS
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    :o

    • one year ago
  33. DLS
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    sin is one function and y other right?

    • one year ago
  34. hartnn
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    cos (a+y) d/dx(a+y) =cos (a+y) (0+dy/dx)

    • one year ago
  35. hartnn
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    yes.

    • one year ago
  36. DLS
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    so I have to treat x&y both as function not variables but other variable like abcd as constants(0) ?

    • one year ago
  37. DLS
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    when differentiating wrt x

    • one year ago
  38. RolyPoly
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    \[\frac{d}{dx}xsin(a+y) \]\[=sin(a+y) \frac{d}{dx}(x) + x\frac{d}{dx}sin(a+y)\]\[=sin(a+y) + x[cos(a+y)\frac{d}{dx}(a+y)]\]\[=sin(a+y) + xcos(a+y)\frac{dy}{dx}\]

    • one year ago
  39. hartnn
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    here since y is the function of x, we treat it as different function. if a is function of x, then a is also function..... if a is independent of x, then a is constant.

    • one year ago
  40. DLS
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    clear!

    • one year ago
  41. hartnn
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    :)

    • one year ago
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