Partial Derivatives > partial derivative of 2xy\sqrt[3]{2x^3+4y}
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∂∂x (2xy3√2x3+4y)=2y(3√2x3+4y+2x3(2x3+4y)23  )
 
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∂ ∂ x (2xy3√2x3+4y)=2y(3√2x3+4y+2x3(2x3+4y)23  )
  • steps
    • ∂ ∂ x (2xy3√2x3+4y)
  • Treat y as a constant
  • Take the constant out:    (a·f)′=a·f ′
    =2y∂ ∂ x (x3√2x3+4y)
  • Apply the Product Rule:    (f·g)′=f ′·g+f·g′
    f=x, g=3√2x3+4y
    =2y(∂ ∂ x (x)3√2x3+4y+∂ ∂ x (3√2x3+4y)x)
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    ∂ ∂ x (x)=1
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    ∂ ∂ x (3√2x3+4y)=2x2(2x3+4y)23  
    =2y(1·3√2x3+4y+2x2(2x3+4y)23  x)
  • show steps
    Simplify 2y(1·3√2x3+4y+2x2(2x3+4y)23  x):    2y(3√2x3+4y+2x3(2x3+4y)23  )
    =2y(3√2x3+4y+2x3(2x3+4y)23  )

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