(32x^6y^4-24x^2y^9+4x^2y)/(4x^2y)

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Solution for (32x^6y^4-24x^2y^9+4x^2y)/(4x^2y) equation:


D( x )

4*x^2*y = 0

4*x^2*y = 0

4*x^2*y = 0

4*x^2*y = 0 // : 4*y

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

(32*x^6*y^4-(24*x^2*y^9)+4*x^2*y)/(4*x^2*y) = 0

(32*x^6*y^4-24*x^2*y^9+4*x^2*y)/(4*x^2*y) = 0

32*x^6*y^4-24*x^2*y^9+4*x^2*y = 0

4*x^2*y*(8*x^4*y^3-6*y^8+1) = 0

8*x^4*y^3 = -(1-6*y^8) // : 8*y^3

x^4 = (-1/8)*y^-3*(1-6*y^8)

x^4 = -1/8*y^-3*(1-6*y^8) // ^ 1/4

abs(x) = (-1/8)^(1/4)*y^(-3/4)*(1-6*y^8)^(1/4)

x = (-1/8)^(1/4)*y^(-3/4)*(1-6*y^8)^(1/4) or x = -((-1/8)^(1/4)*y^(-3/4)*(1-6*y^8)^(1/4))

4*x^2*y = 0

4*x^2*y = 0 // : 4*y

x^2 = 0

x = 0

x in { 0}

x in { (-1/8)^(1/4)*y^(-3/4)*(1-6*y^8)^(1/4), -((-1/8)^(1/4)*y^(-3/4)*(1-6*y^8)^(1/4)) }

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