Derivatives > derivative of 1/(2sqrt(x+1))
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ddx (12√x+1 )=−14(x+1)32  
 
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ddx (12√x+1 )=−14(x+1)32  
  • steps
    • ddx (12√x+1 )
  • Take the constant out:    (a·f)′=a·f ′
    =12 ddx (1√x+1 )
  • Apply exponent rule:    1a =a−1
    =12 ddx ((x+1)−12 )
  • show steps
    Apply the chain rule:    −12(x+1)32  ddx (x+1)
    =−12(x+1)32  ddx (x+1)
  • show steps
    ddx (x+1)=1
    =12 (−12(x+1)32  · 1)
  • show steps
    Simplify 12 (−12(x+1)32  · 1):    −14(x+1)32  
    =−14(x+1)32  

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