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Find dy/dx by implicit differentiation.

x^3+8x+x^13y-y^6=4

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3x^2 + 8 + 13x^12y + x^13y' - 6y^5y' = 0
now just collect terms and solve for y'

dy/dx = 3x^2+8+13x^12y / 6y^5-x^13

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