Partial Derivatives > (\partial)/(\partial x)((x+y)/(x-y))
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∂∂x (x+yx−y )=−2y(x−y)2 
 
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∂ ∂ x (x+yx−y )=−2y(x−y)2 
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    • ∂ ∂ x (x+yx−y )
  • Treat y as a constant
  • Apply the Quotient Rule:    (fg )′=f ′·g−g′·fg2 
    =∂ ∂ x (x+y)(x−y)−∂ ∂ x (x−y)(x+y)(x−y)2 
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    ∂ ∂ x (x+y)=1
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    ∂ ∂ x (x−y)=1
    =1·(x−y)−1·(x+y)(x−y)2 
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    Simplify 1·(x−y)−1·(x+y)(x−y)2 :    −2y(x−y)2 
    =−2y(x−y)2 

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