Partial Derivatives > partial derivative of x/(y^2+x^2)
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∂∂y (xy2+x2 )=−2xy(y2+x2)2 
 
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∂ ∂ y (xy2+x2 )=−2xy(y2+x2)2 
  • steps
    • ∂ ∂ y (xy2+x2 )
  • Treat x as a constant
  • Take the constant out:    (a·f)′=a·f ′
    =x∂ ∂ y (1y2+x2 )
  • Apply exponent rule:    1a =a−1
    =x∂ ∂ y ((y2+x2)−1)
  • show steps
    Apply the chain rule:    −1(y2+x2)2 ∂ ∂ y (y2+x2)
    =−1(y2+x2)2 ∂ ∂ y (y2+x2)
  • show steps
    ∂ ∂ y (y2+x2)=2y
    =x(−1(y2+x2)2 · 2y)
  • show steps
    Simplify x(−1(y2+x2)2 · 2y):    −2xy(y2+x2)2 
    =−2xy(y2+x2)2 

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