Implicit Derivatives > implicit derivative of (d^2y)/(dx^2), y=xy^2+x^2y
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ImplicitDerivatived2ydx2 ofy=xy2+x2y:    −6xy4−12x2y3+4y3−12x3y2+4xy2−6x4y+4x2y+2y(1−2xy−x2)3 
 
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Implicit Derivative d2ydx2  of y=xy2+x2y:    −6xy4−12x2y3+4y3−12x3y2+4xy2−6x4y+4x2y+2y(1−2xy−x2)3 
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    • y=xy2+x2y
  • Treat y as y(x)
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    Implicit Derivative dydx  of y=xy2+x2y:    y2+2xy1−2xy−x2 
  • dydx =y2+2xy1−2xy−x2 
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    Implicit Derivative d2ydx2  of dydx =y2+2xy1−2xy−x2 :    −2x3dydx −2x2ydydx +2x2y−2xy2dydx +2xdydx +2xy2+2ydydx +2y+2y3(1−2xy−x2)2 
  • d2ydx2 =−2x3dydx −2x2ydydx +2x2y−2xy2dydx +2xdydx +2xy2+2ydydx +2y+2y3(1−2xy−x2)2 
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    Substitute dydx =y2+2xy1−2xy−x2 :    −6xy4−12x2y3+4y3−12x3y2+4xy2−6x4y+4x2y+2y(1−2xy−x2)3 
    d2ydx2 =−6xy4−12x2y3+4y3−12x3y2+4xy2−6x4y+4x2y+2y(1−2xy−x2)3 

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