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anonymous

  • 5 years ago

can anybody solve partial deriavative z=e^x^2 + xy with respect to x and y

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  1. Yuki
    • 5 years ago
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    yes let's find f_x first

  2. anonymous
    • 5 years ago
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    When you take the partial derivative with respect to x, consider y as a constant.

  3. Yuki
    • 5 years ago
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    \[f = e^{x^2} + xy \] \[f_x = 2x*e^{x^2} + y\]

  4. anonymous
    • 5 years ago
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    \[{\partial z \over \partial x}=2xe^{x^2}+y\]

  5. Yuki
    • 5 years ago
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    \[f_y = 0 + x = x\]

  6. anonymous
    • 5 years ago
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    \[{\partial z \over \partial y}=x\]

  7. Yuki
    • 5 years ago
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    Anwar you always surprise me. How did you get that "d" from ?!

  8. Yuki
    • 5 years ago
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    Anwar you always surprise me. How did you get that "d" from ?!\[\partial\]

  9. anonymous
    • 5 years ago
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    Try to find out yourself :)

  10. anonymous
    • 5 years ago
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    cool !!!

  11. anonymous
    • 5 years ago
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    lol that was fast :)

  12. Yuki
    • 5 years ago
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    that was a lot easier than I thought lol

  13. anonymous
    • 5 years ago
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    Haha yeah

  14. Yuki
    • 5 years ago
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    anyway, zizUo, with partial derivatives you will treat the other variable as same as numbers, so for f_y, the term \[e^{x^2}\] has no y in it, so it's derivative is 0 since you treat is as if it's a number

  15. Yuki
    • 5 years ago
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    so it is actually not that hard. implicit differentiation is much more harder :)

  16. anonymous
    • 5 years ago
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    it means u simply have to separate out the e^x ?

  17. Yuki
    • 5 years ago
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    e^x^2 has no y in it, so the partial derivative of e^x^2 with respect to y, is as same as taking the derivative of a number like 10 or 34

  18. Yuki
    • 5 years ago
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    on the other hand, the term xy has a y multiplied to x, so it is similar to saying " find the derivative of 2y" which is 2 in our case, x is the constant, so the partial derivative of xy is x

  19. Yuki
    • 5 years ago
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    on the other hand, the term xy has a y multiplied to x, so it is similar to saying " find the derivative of 2y" which is 2 in our case, x is the constant, so the partial derivative of xy is x

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