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calyne

  • 4 years ago

Find y' by implicit differentiation: 1/x + 1/y = 1

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  1. .Sam.
    • 4 years ago
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    \[\frac{1}{x}+\frac{1}{y}=1\] \[x^{-1}+y^{-1}=1\] -------------------------------------- Differentiate, \[-x^{-2}-y^{-2}(y')=0\] \[-y^{-2}(y')=x^{-2}\] \[(y')=\frac{x^{-2}}{-y^{-2}}\] \[y'=-\frac{y^2}{x^2}\]

  2. calyne
    • 4 years ago
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    Okay so now: Solve the equation explicitly for y and differentiate to get y' in terms of x.

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