What is the tangent of xy2=2+xy ?

The tangent of xy2=2+xy is y=-2/(a_{0)^2}x+4/(a_{0)}

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tangent of xy2=2+xy

tangent of

x y 2 = 2 + x y

y = - \frac{2}{a _{0}^{2}} x + \frac{4}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0}})

Find the slope of

x y 2 = 2 + x y : \frac{d y}{d x} = - \frac{2}{x ^{2}}

Compute the slope of

x y 2 = 2 + x y

x = a_{0} : m = - \frac{2}{a _{0}^{2}}

Find the line with slope m=

- \frac{2}{a _{0}^{2}}

and passing through

(a_{0}, \frac{2}{a _{0}}) : y = - \frac{2}{a _{0}^{2}} x + \frac{4}{a _{0}}

y = - \frac{2}{a _{0}^{2}} x + \frac{4}{a _{0}}

\int_{0}^{1} 2 x^{2} d x

\int \frac{1}{x ^{2} - 2 x - 8} d x

f (x) = x^{2} - 20 x, g (x) = 0

\frac{d}{d x} (ln (\frac{1}{6 x}))

(ln (1 - 7 x))^{^{'}}

What is the tangent of xy2=2+xy ?
The tangent of xy2=2+xy is y=-2/(a_{0)^2}x+4/(a_{0)}