Derivatives > derivative of-(2x/((1+x^2)^2))
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ddx (−2x(1+x2)2 )=−2(−3x2+1)(1+x2)3 
 
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ddx (−2x(1+x2)2 )=−2(−3x2+1)(1+x2)3 
  • steps
    • ddx (−2x(1+x2)2 )
  • Take the constant out:    (a·f)′=a·f ′
    =−2ddx (x(1+x2)2 )
  • Apply the Quotient Rule:    (fg )′=f ′·g−g′·fg2 
    =−2·dxdx (1+x2)2−ddx ((1+x2)2)x((1+x2)2)2 
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    dxdx =1
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    ddx ((1+x2)2)=4x(1+x2)
    =−2·1·(1+x2)2−4x(1+x2)x((1+x2)2)2 
  • show steps
    Simplify −2·1·(1+x2)2−4x(1+x2)x((1+x2)2)2 :    −2(−3x2+1)(1+x2)3 
    =−2(−3x2+1)(1+x2)3 

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