What is the tangent of x^3+y^3=7xy,(2,-4) ?

The tangent of x^3+y^3=7xy,(2,-4) is y=-20/17 x-28/17

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tangent of x^3+y^3=7xy,(2,-4)

tangent of

x^{3} + y^{3} = 7 x y, (2, - 4)

y = - \frac{20}{17} x - \frac{28}{17}

Solution steps

Find the slope of

x^{3} + y^{3} = 7 x y : \frac{d y}{d x} = \frac{7 y - 3 x ^{2}}{3 y ^{2} - 7 x}

Compute the slope of

x^{3} + y^{3} = 7 x y

(2, - 4) : m = - \frac{20}{17}

Find the line with slope m=

- \frac{20}{17}

and passing through

(2, - 4) : y = - \frac{20}{17} x - \frac{28}{17}

y = - \frac{20}{17} x - \frac{28}{17}

y = \frac{1}{x ^{2}}, (- 1, 1)

\int_{\frac{1}{5}}^{7} 12 x ln (5 x) d x

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

\frac{d}{d x} (\frac{ln ( 2 x )}{5 x})

\int cos^{2} (\frac{1}{2} x) d x

What is the tangent of x^3+y^3=7xy,(2,-4) ?
The tangent of x^3+y^3=7xy,(2,-4) is y=-20/17 x-28/17