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What is the derivative dy/dx given that y^3*x^2 = 1

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b52 | Student, Grade 9 | (Level 2) eNoter

Posted June 22, 2013 at 2:13 PM via web

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What is the derivative dy/dx given that y^3*x^2 = 1

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 22, 2013 at 2:17 PM (Answer #1)

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The derivative `dy/dx` has to be derived for y^3*x^2 = 1.

`(d(y^3*x^2))/dx = 0`

=>` y^3*2x + 3y^2*x^2*(dy/dx) = 0`

=> `3y^2*x^2*(dy/dx) = (-y^3*2x)`

=> `(dy/dx) = (-y^3*2x)/(3y^2*x^2)`

=> `(dy/dx) = (-y*2)/(3*x)`

The required derivative is `(dy/dx) = (-2*y)/(3*x)`

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