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How do you implicitly differentiate #-1=5y^3x-2xy+3x^2y #?

1 Answer

Mar 11, 2018

#dy/dx= -(5y^3 -2y +6xy)/(15xy^2 -2x +3x^3)#

Explanation:

Differentiate both sides terms wise
#(d/dx -1)= 5d/dx y^3 x -2 d/dx xy +3 d/dx x^2y#

#0=5(y^3 +x 3y^2 dy/dx)-2(y +x dy/dx) +3(2xy +x^2 dy/dx)#

#0=(5y^3 -2y +6xy)+(15xy^2 -2x +3x^3 )dy/dx#

#dy/dx= -(5y^3 -2y +6xy)/(15xy^2 -2x +3x^3)#

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