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anonymous

  • 5 years ago

Implicit differentiation, equation to follow

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  1. anonymous
    • 5 years ago
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    \[\sqrt{x}+\sqrt{y}=5\]

  2. anonymous
    • 5 years ago
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    Would this just be \[x^1/2+y^1/2=\]

  3. heisenberg
    • 5 years ago
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    what are you attempting to derive?

  4. anonymous
    • 5 years ago
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    i am trying to find dy/dx of the above equation

  5. heisenberg
    • 5 years ago
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    it's been a while so i may be fuzzy, but the basic gist is: 1. Since we are doing dy/dx, treat all 'x's as constant and take the derivative. 2. When you derive a 'y' term, also include a dy/dx 3. solve for dy/dx

  6. heisenberg
    • 5 years ago
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    so i THINK: \[x^\frac{1}{2} + \frac{1}{2}*y^\frac{-1}{2}*\frac{dy}{dx} = 0\]

  7. heisenberg
    • 5 years ago
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    \[\frac{dy}{dx} = - 2 * \sqrt y * \sqrt x\]

  8. anonymous
    • 5 years ago
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    Think you are mixing up you partial differentiation with your single variable calculus

  9. anonymous
    • 5 years ago
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    In single variable cal, you differentiate the x also

  10. anonymous
    • 5 years ago
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    so would the fourmula be\[x+dy/dx+y+dy/dx\]

  11. heisenberg
    • 5 years ago
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    i don't know that you have to use implicit differentiation to solve this actually. can't you just solve for y and then derive?

  12. anonymous
    • 5 years ago
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    start from the top. Differentiate each item; the y item you write in dy/dx next to it. Solve for dy/dx. There is no formula per se zbay. You differentiate and then solve for dy/dx

  13. anonymous
    • 5 years ago
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    ok thanks let me attempt to work it out

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