(4x^5y^3-12x^3)/(8v^6x^6)

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Solution for (4x^5y^3-12x^3)/(8v^6x^6) equation:


D( x )

8*v^6*x^6 = 0

8*v^6*x^6 = 0

8*v^6*x^6 = 0

8*v^6*x^6 = 0 // : 8*v^6

x^6 = 0

x = 0

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

(4*x^5*y^3-(12*x^3))/(8*v^6*x^6) = 0

(4*x^5*y^3-12*x^3)/(8*v^6*x^6) = 0

4*x^5*y^3-12*x^3 = 0

4*x^3*(x^2*y^3-3) = 0

x^2*y^3 = 3 // : y^3

x^2 = 3/(y^3)

x^2 = 3/(y^3) // ^ 1/2

abs(x) = (3^(1/2))/(y^(3/2))

x = (3^(1/2))/(y^(3/2)) or x = -((3^(1/2))/(y^(3/2)))

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

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

( 4*x^3 )

4*x^3 = 0 // : 4

x^3 = 0

x = 0

( x+3^(1/2)*y^(-3/2) )

x+3^(1/2)*y^(-3/2) = 0 // - 3^(1/2)*y^(-3/2)

x = -(3^(1/2)*y^(-3/2))

( x-3^(1/2)*y^(-3/2) )

x-3^(1/2)*y^(-3/2) = 0 // + -3^(1/2)*y^(-3/2)

x = -(-3^(1/2)*y^(-3/2))

x in { 0}

x in { -(3^(1/2)*y^(-3/2)), -(-3^(1/2)*y^(-3/2)) }

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