What is the slope of 2xy^3=xy+6 ?

The slope of 2xy^3=xy+6 is (y-2y^3)/(x(-1+6y^2))

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slope of 2xy^3=xy+6

slope

2 x y^{3} = x y + 6

\frac{y - 2 y ^{3}}{x ( - 1 + 6 y ^{2} )}

Solution steps

2 x y^{3} = x y + 6

Use implicit differentiation to find the slope of

2 x y^{3} = x y + 6

Implicit Derivative

\frac{d y}{d x}

2 x y^{3} = x y + 6 : \frac{y - 2 y ^{3}}{x ( - 1 + 6 y ^{2} )}

\frac{y - 2 y ^{3}}{x ( - 1 + 6 y ^{2} )}

\int \frac{1}{4 x} + 9 d x

y^{^{'}} = \frac{( x ^{4} + x ^{2} y ^{2} + y ^{4} )}{x ^{3} y}

t - 2

y = lo g_{6} (x)

x \to 2 lim (x^{2})

What is the slope of 2xy^3=xy+6 ?
The slope of 2xy^3=xy+6 is (y-2y^3)/(x(-1+6y^2))