Find dy/dx by implicit differentiation.x^6(x + y) = y^2(4x − y)

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cosinusix | College Teacher | (Level 3) Assistant Educator

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Think that y is a function of x and differentiate with respect to the variable x using usual differentiation rules.

 

`6x^5(x+y)+x^6(1+y')=2y'y(4x-y)+y^2(4-y')`

 

`7x^6+6x^5y+x^6y'=8y'yx-3y'y^2)+4y^2`

 

Solve for y':

 

`y'(x^6-8yx+3y^2)=4y^2-7x^6-6x^5y`

Solution `y'=(dy)/(dx)=(4y^2-7x^6-6x^5y)/(x^6-8yx+3y^2)`

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