What is the tangent of y=x^{8/5} ?

The tangent of y=x^{8/5} is y=(8a_{0}^{3/5})/5 x+a_{0}^{8/5}-(8a_{0}^{8/5})/5

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tangent of y=x^{8/5}

tangent of

y = x^{\frac{8}{5}}

y = \frac{8 a _{0}^{\frac{3}{5}}}{5} x + a_{0}^{\frac{8}{5}} - \frac{8 a _{0}^{\frac{8}{5}}}{5}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{\frac{8}{5}})

Find the slope of

y = x^{\frac{8}{5}} : \frac{d y}{d x} = \frac{8 x ^{\frac{3}{5}}}{5}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{8 a _{0}^{\frac{3}{5}}}{5}

Find the line with slope m=

\frac{8 a _{0}^{\frac{3}{5}}}{5}

and passing through

(a_{0}, a_{0}^{\frac{8}{5}}) : y = \frac{8 a _{0}^{\frac{3}{5}}}{5} x + a_{0}^{\frac{8}{5}} - \frac{8 a _{0}^{\frac{8}{5}}}{5}

y = \frac{8 a _{0}^{\frac{3}{5}}}{5} x + a_{0}^{\frac{8}{5}} - \frac{8 a _{0}^{\frac{8}{5}}}{5}

x \to 1 lim (e^{5 x^{5} - 5 x})

\int_{0}^{π} 1 - cos (2 x) d x

\int 2 x + 3 d x

\frac{d}{d x} (e^{s i n (x)} cos (sin (x)))

\frac{d}{d x} (e^{0.1 x})

What is the tangent of y=x^{8/5} ?
The tangent of y=x^{8/5} is y=(8a_{0}^{3/5})/5 x+a_{0}^{8/5}-(8a_{0}^{8/5})/5