What is the tangent of 1/(x^5) ?

The tangent of 1/(x^5) is y=-5/(a_{0)^6}x+6/(a_{0)^5}

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tangent of 1/(x^5)

tangent of

\frac{1}{x ^{5}}

y = - \frac{5}{a _{0}^{6}} x + \frac{6}{a _{0}^{5}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{1}{a _{0}^{5}})

Find the slope of

y = \frac{1}{x ^{5}} : \frac{d y}{d x} = - \frac{5}{x ^{6}}

Compute the slope of

y = \frac{1}{x ^{5}}

x = a_{0} : m = - \frac{5}{a _{0}^{6}}

Find the line with slope m=

- \frac{5}{a _{0}^{6}}

and passing through

(a_{0}, \frac{1}{a _{0}^{5}}) : y = - \frac{5}{a _{0}^{6}} x + \frac{6}{a _{0}^{5}}

y = - \frac{5}{a _{0}^{6}} x + \frac{6}{a _{0}^{5}}

\int (x + 1) (2 x^{2} + x) d x

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} = 0

x \to - 3 lim (\frac{3 - ∣ x ∣}{3 + x})

y^{^{''}} + 6 y^{^{'}} + 34 y = 25 e^{- 3 x}

\frac{d}{d x} (4 x - 5 x^{\frac{5}{6}})

What is the tangent of 1/(x^5) ?
The tangent of 1/(x^5) is y=-5/(a_{0)^6}x+6/(a_{0)^5}