What is the tangent of y=x^{-1/7},(1,1) ?

The tangent of y=x^{-1/7},(1,1) is y=-1/7 x+8/7

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tangent of y=x^{-1/7},(1,1)

tangent of

y = x^{- \frac{1}{7}}, (1, 1)

y = - \frac{1}{7} x + \frac{8}{7}

Solution steps

Find the slope of

y = x^{- \frac{1}{7}} : \frac{d y}{d x} = - \frac{1}{7 x ^{\frac{8}{7}}}

Compute the slope of

y = x^{- \frac{1}{7}}

(1, 1) : m = - \frac{1}{7}

Find the line with slope m=

- \frac{1}{7}

and passing through

(1, 1) : y = - \frac{1}{7} x + \frac{8}{7}

y = - \frac{1}{7} x + \frac{8}{7}

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

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 3) x^{2})

\frac{d}{d x} (- 2 x^{- 3})

g^{'} (x)

\int - \frac{6}{x} d x

What is the tangent of y=x^{-1/7},(1,1) ?
The tangent of y=x^{-1/7},(1,1) is y=-1/7 x+8/7