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imagreencat

  • 3 years ago

Hey guys! I would just like to ask if my partial differentiating is correct. f(x,y)=xy (sin (4yx^2)) fyx = sin 4yx^2 + (8yx^2)(cos 4yx^2) + (12yx^2)(cos 4yx^2) - 32(x^4)(y^2)(sin 4yx^2) Thanks!

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  1. ash2326
    • 3 years ago
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    You have differentiated with respect to x or y?

  2. imagreencat
    • 3 years ago
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    Well, fyx. So I first diff with respect to y then with respect to x. :)

  3. TuringTest
    • 3 years ago
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    it's the mixed derivative? let me check...

  4. ash2326
    • 3 years ago
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    Ok :)

  5. TuringTest
    • 3 years ago
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    \[f_x=y\sin(4yx^2)+8x^2y^2\sin(4x^2y)\cos(4x^2y)\]I'm typing it out so we can all see if I make a mistake...

  6. imagreencat
    • 3 years ago
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    Fy first. :) Then diff Fy with respect to x.

  7. TuringTest
    • 3 years ago
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    the order shouldn't matter I don't think\[f_{xy}=\sin(4yx^2)+4yx^2\cos(4yx^2)+\frac{\partial}{\partial y}[8x^2y^2\sin(4x^2y)\cos(4x^2y)]\]

  8. imagreencat
    • 3 years ago
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    Actually in some cases the order does not matter. But in others, it does. Anyway, thank you turing test! :)

  9. TuringTest
    • 3 years ago
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    oh but I have a 16...

  10. TuringTest
    • 3 years ago
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    I'll do it the other way on paper to see if that makes a diff

  11. TuringTest
    • 3 years ago
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    ok I redid it the other way and got the same answer as you sorry for the confusion

  12. imagreencat
    • 3 years ago
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    It's okay Turing Test. I'm sorry for taking some of your time. :))) But, thanks again. I appreciate your effort.

  13. TuringTest
    • 3 years ago
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    no it's my fault for messing up the first time you're welcome

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