How do you differentiate x^4(x+y)=y^2(3x-y)?

1 Answer
bp
Sep 11, 2015

dy/dx=(3y^2-5x^4-4x^3y)/(x^4 -6xy+3y^2)

Explanation:

This can be by implicit differentiation. Rewrite it as x^5+x^4 y= 3xy^2 - y^3. Now differentiate term wise, 5x^4 +x^4 dy/dx + 4x^3 y= 3y^2+6xydy/dx-3y^2 dy/dx

(x^4 -6xy+3y^2)dy/dx=3y^2-5x^4-4x^3y

dy/dx=(3y^2-5x^4-4x^3y)/(x^4 -6xy+3y^2)

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